reserve X for non empty set;
reserve Y for ComplexLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);
reserve a,b for Complex;
reserve u,v,w for VECTOR of CLSStruct(#Funcs(X,the carrier of Y), (FuncZero(X,
    Y)),FuncAdd(X,Y),FuncExtMult(X,Y)#);

theorem Th38:
  for X,Y be ComplexNormSpace holds
  C_NormSpace_of_BoundedLinearOperators(X,Y) is ComplexNormSpace
proof
  let X,Y be ComplexNormSpace;
  CLSStruct (# BoundedLinearOperators(X,Y), Zero_(BoundedLinearOperators(X
,Y), C_VectorSpace_of_LinearOperators(X,Y)), Add_(BoundedLinearOperators(X,Y),
    C_VectorSpace_of_LinearOperators(X,Y)), Mult_(BoundedLinearOperators(X,Y),
    C_VectorSpace_of_LinearOperators(X,Y)) #) is ComplexLinearSpace;
  hence thesis by Th37,CSSPACE3:2;
end;
