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 Th37:
  for X,Y be ComplexNormSpace holds
  C_NormSpace_of_BoundedLinearOperators(X,Y) is
   reflexive discerning ComplexNormSpace-like
proof
  let X,Y be ComplexNormSpace;
  thus C_NormSpace_of_BoundedLinearOperators(X,Y) is reflexive
   by Th36;
  for x, y being Point of C_NormSpace_of_BoundedLinearOperators(X,Y) for c
be Complex holds ( ||.x.|| = 0 iff x = 0.C_NormSpace_of_BoundedLinearOperators(
X,Y) ) & ||.c*x.|| = |.c.| * ||.x.|| & ||.x+y.|| <= ||.x.|| + ||.y.|| by Th36;
  hence thesis by CLVECT_1:def 13;
end;
