theorem Th39:
  for X, Y be RealNormSpace holds
  R_NormSpace_of_BoundedLinearOperators(X,Y) is RealNormSpace
proof
  let X, Y be RealNormSpace;
  RLSStruct (# BoundedLinearOperators(X,Y), Zero_(BoundedLinearOperators(X
,Y), R_VectorSpace_of_LinearOperators(X,Y)), Add_(BoundedLinearOperators(X,Y),
    R_VectorSpace_of_LinearOperators(X,Y)), Mult_(BoundedLinearOperators(X,Y),
    R_VectorSpace_of_LinearOperators(X,Y)) #) is RealLinearSpace;
  hence thesis by Th38,RSSPACE3:2;
end;
