begin
theorem
for
X,
Y,
Z being ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace)
for
f being ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
Y : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
for
g being ( (
Function-like V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ) ( non
empty V13()
V16( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) )
LinearOperator of
Y : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
Z : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) holds
g : ( (
Function-like V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ) ( non
empty V13()
V16( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) )
LinearOperator of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
* f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) : ( (
Function-like ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ComplexLinearSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ComplexLinearSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) is ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ,
Z : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
ComplexLinearSpace) ) ;
theorem
for
X,
Y,
Z being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f being ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
Y : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
for
g being ( (
Function-like V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
Y : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
Z : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) holds
(
g : ( (
Function-like V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
* f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b2 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( (
Function-like ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) is ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
Z : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) & ( for
x being ( ( ) (
right_complementable )
VECTOR of ( ( ) ( non
empty )
set ) ) holds
(
||.((g : ( ( Function-like V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) * f : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( ( Function-like ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( right_complementable ) VECTOR of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( right_complementable ) Element of the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) .|| : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
<= (((BoundedLinearOperatorsNorm (Y : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,Z : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( Function-like V27( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) ) ( non empty V13() V16( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V17( REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) Function-like V23( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V27( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) V35() V36() V37() ) Element of bool [:(BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) ( V35() V36() V37() ) set ) : ( ( ) ( ) set ) ) . g : ( ( Function-like V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( ( ) ( complex real ext-real ) set ) * ((BoundedLinearOperatorsNorm (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,Y : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( Function-like V27( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) ) ( non empty V13() V16( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V17( REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) Function-like V23( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V27( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) V35() V36() V37() ) Element of bool [:(BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) ( V35() V36() V37() ) set ) : ( ( ) ( ) set ) ) . f : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( ( ) ( complex real ext-real ) set ) ) : ( ( ) (
complex real ext-real )
set )
* ||.x : ( ( ) ( right_complementable ) VECTOR of ( ( ) ( non empty ) set ) ) .|| : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) ) &
(BoundedLinearOperatorsNorm (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,Z : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( (
Function-like V27(
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) ) ) ( non
empty V13()
V16(
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
Function-like V23(
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V27(
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
V35()
V36()
V37() )
Element of
bool [:(BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) (
V35()
V36()
V37() )
set ) : ( ( ) ( )
set ) )
. (g : ( ( Function-like V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) * f : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( (
Function-like ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b3 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
complex real ext-real )
set )
<= ((BoundedLinearOperatorsNorm (Y : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,Z : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( Function-like V27( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) ) ( non empty V13() V16( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V17( REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) Function-like V23( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V27( BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) V35() V36() V37() ) Element of bool [:(BoundedLinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) ( V35() V36() V37() ) set ) : ( ( ) ( ) set ) ) . g : ( ( Function-like V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b3 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( ( ) (
complex real ext-real )
set )
* ((BoundedLinearOperatorsNorm (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,Y : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( Function-like V27( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) ) ( non empty V13() V16( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V17( REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) Function-like V23( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) V27( BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) ) V35() V36() V37() ) Element of bool [:(BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) ( V35() V36() V37() ) set ) : ( ( ) ( ) set ) ) . f : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b2 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( ( ) (
complex real ext-real )
set ) : ( ( ) (
complex real ext-real )
set ) ) ) ) ;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
let f,
g be ( (
Function-like V27( the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) ;
*redefine func g * f -> ( (
Function-like V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V17( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
Function-like V23( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian )
LinearOperator of
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) ;
end;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
let f,
g be ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
func f + g -> ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
equals
(Add_ ((BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
. (
f : ( ( ) ( )
VectSpStr over
X : ( ( ) ( )
ComplexAlgebraStr ) ) ,
g : ( (
Function-like V27(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) ) (
V13()
V16(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) )
V17(
X : ( ( ) ( )
ComplexAlgebraStr ) )
Function-like V27(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) )
Element of
bool [:[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
end;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
let f,
g be ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
func g * f -> ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
equals
(modetrans (g : ( ( Function-like V27([:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) ComplexAlgebraStr ) ) ) ( V13() V16([:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ) V17(X : ( ( ) ( ) ComplexAlgebraStr ) ) Function-like V27([:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) ComplexAlgebraStr ) ) ) Element of bool [:[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) ,X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( (
Function-like V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V17( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
Function-like V23( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian )
Element of
bool [: the carrier of X : ( ( ) ( ) ComplexAlgebraStr ) : ( ( ) ( ) set ) , the carrier of X : ( ( ) ( ) ComplexAlgebraStr ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
* (modetrans (f : ( ( ) ( ) VectSpStr over X : ( ( ) ( ) ComplexAlgebraStr ) ) ,X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( (
Function-like V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V17( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
Function-like V23( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian )
Element of
bool [: the carrier of X : ( ( ) ( ) ComplexAlgebraStr ) : ( ( ) ( ) set ) , the carrier of X : ( ( ) ( ) ComplexAlgebraStr ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( (
Function-like V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V17( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
Function-like V23( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V27( the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) , the
carrier of
X : ( ( ) ( )
ComplexAlgebraStr ) : ( ( ) ( )
set ) )
V171(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
V172(
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) )
Lipschitzian )
LinearOperator of
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) ;
end;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
let f be ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
let z be ( (
complex ) (
complex )
Complex) ;
func z * f -> ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
equals
(Mult_ ((BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
. (
z : ( (
Function-like V27(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) ) (
V13()
V16(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) )
V17(
X : ( ( ) ( )
ComplexAlgebraStr ) )
Function-like V27(
[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) )
Element of
bool [:[:X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) ComplexAlgebraStr ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
f : ( ( ) ( )
VectSpStr over
X : ( ( ) ( )
ComplexAlgebraStr ) ) ) : ( ( ) ( )
set ) ;
end;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
func FuncMult X -> ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V23(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
BinOp of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
means
for
f,
g being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) holds
it : ( ( ) ( )
VectSpStr over
X : ( ( ) ( )
ComplexAlgebraStr ) )
. (
f : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
g : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= f : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* g : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
end;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g,
h being ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) holds
(
h : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
= f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
* g : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) iff for
x being ( ( ) (
right_complementable )
VECTOR of ( ( ) ( non
empty )
set ) ) holds
h : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
. x : ( ( ) (
right_complementable )
VECTOR of ( ( ) ( non
empty )
set ) ) : ( ( ) (
right_complementable )
Element of the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
= f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
. (g : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) . x : ( ( ) ( right_complementable ) VECTOR of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
right_complementable )
Element of the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
right_complementable )
Element of the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g,
h being ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) holds
f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
* (g : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) * h : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
= (f : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) * g : ( ( Function-like V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) ( non empty V13() V16( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V17( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) Function-like V23( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V27( the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) V171(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) V172(b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) Lipschitzian ) LinearOperator of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) ) : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
* h : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f being ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) holds
(
f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
* (id the carrier of X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) : ( (
V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like one-to-one V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( (
Function-like ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
= f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) &
(id the carrier of X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) ) : ( (
V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like one-to-one V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
* f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( (
Function-like ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
= f : ( (
Function-like V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V17( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
Function-like V23( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V27( the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty )
set ) )
V171(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
V172(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) )
Lipschitzian )
LinearOperator of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g,
h being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) holds
f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* (g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= (f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* h : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) holds
(
f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* (FuncUnit X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) &
(FuncUnit X : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g,
h being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) holds
f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* (g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) + h : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= (f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
+ (f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g,
h being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) holds
(g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) + h : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* f : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= (g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
+ (h : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
for
a,
b being ( (
complex ) (
complex )
Complex) holds
(a : ( ( complex ) ( complex ) Complex) * b : ( ( complex ) ( complex ) Complex) ) : ( ( ) (
complex )
set )
* (f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= (a : ( ( complex ) ( complex ) Complex) * f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* (b : ( ( complex ) ( complex ) Complex) * g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
X being ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace)
for
f,
g being ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
X : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
for
a being ( (
complex ) (
complex )
Complex) holds
a : ( (
complex ) (
complex )
Complex)
* (f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) * g : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
= (a : ( ( complex ) ( complex ) Complex) * f : ( ( ) ( ) Element of BoundedLinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
* g : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
func Ring_of_BoundedLinearOperators X -> ( ( ) ( )
doubleLoopStr )
equals
doubleLoopStr(#
(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
(Add_ ((BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
(FuncMult X : ( ( ) ( ) ComplexAlgebraStr ) ) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V23(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
BinOp of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(FuncUnit X : ( ( ) ( ) ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(Zero_ ((BoundedLinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
ComplexAlgebraStr ) ,
X : ( ( ) ( )
ComplexAlgebraStr ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) ComplexAlgebraStr ) ,X : ( ( ) ( ) ComplexAlgebraStr ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) #) : ( (
strict ) (
strict )
doubleLoopStr ) ;
end;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
func C_Algebra_of_BoundedLinearOperators X -> ( ( ) ( )
ComplexAlgebraStr )
equals
ComplexAlgebraStr(#
(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
(FuncMult X : ( ( ) ( ) set ) ) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V23(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
BinOp of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(Add_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
(Mult_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
(FuncUnit X : ( ( ) ( ) set ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(Zero_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) #) : ( (
strict ) (
strict )
ComplexAlgebraStr ) ;
end;
theorem
for
X being ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) holds
(BoundedLinearOperatorsNorm (X : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,X : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( (
Function-like V27(
BoundedLinearOperators (
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) ) ) ( non
empty V13()
V16(
BoundedLinearOperators (
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
Function-like V23(
BoundedLinearOperators (
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V27(
BoundedLinearOperators (
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ,
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ) : ( ( ) ( non
empty )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
V35()
V36()
V37() )
Element of
bool [:(BoundedLinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( ) ( non empty ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) ,b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) (
V35()
V36()
V37() )
set ) : ( ( ) ( )
set ) )
. (id the carrier of X : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty non trivial ) set ) ) : ( (
V23( the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) ) ( non
empty V13()
V16( the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V17( the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
Function-like one-to-one V23( the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) )
V27( the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) , the
carrier of
b1 : ( ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty non
trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) : ( ( ) ( non
empty non
trivial )
set ) ) )
Element of
bool [: the carrier of b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty non trivial ) set ) , the carrier of b1 : ( ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ComplexNormSpace) : ( ( ) ( non empty non trivial ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
complex real ext-real )
set )
= 1 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural complex real V30()
V31()
ext-real positive non
negative V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
bool REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) : ( ( ) ( )
set ) ) ) ;
definition
let X be ( ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like )
ComplexNormSpace) ;
func C_Normed_Algebra_of_BoundedLinearOperators X -> ( ( ) ( )
Normed_Complex_AlgebraStr )
equals
Normed_Complex_AlgebraStr(#
(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
(FuncMult X : ( ( ) ( ) set ) ) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V23(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
BinOp of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(Add_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
(Mult_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( (
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ) (
V13()
V16(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) )
V17(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Function-like V27(
[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) ,
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) )
Element of
bool [:[:COMPLEX : ( ( ) ( non empty V46() V57() V63() ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) ,(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
(FuncUnit X : ( ( ) ( ) set ) ) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(Zero_ ((BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) )) : ( ( ) ( )
Element of
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) ,
(BoundedLinearOperatorsNorm (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( (
Function-like V27(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) ) ) ( non
empty V13()
V16(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
Function-like V23(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
V27(
BoundedLinearOperators (
X : ( ( ) ( )
set ) ,
X : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
bool the
carrier of
(C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital )
CLSStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) ( non
empty V46()
V57()
V58()
V59()
V63() )
set ) )
V35()
V36()
V37() )
Element of
bool [:(BoundedLinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool the carrier of (C_VectorSpace_of_LinearOperators (X : ( ( ) ( ) set ) ,X : ( ( ) ( ) set ) )) : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) CLSStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty V46() V57() V58() V59() V63() ) set ) :] : ( ( ) (
V35()
V36()
V37() )
set ) : ( ( ) ( )
set ) ) #) : ( (
strict ) (
strict )
Normed_Complex_AlgebraStr ) ;
end;