
theorem Th39:
  for X being RealNormSpace-Sequence,Y be RealNormSpace
  holds R_NormSpace_of_BoundedMultilinearOperators(X,Y) is RealNormSpace
  proof
    let X be RealNormSpace-Sequence,Y be RealNormSpace;
    RLSStruct (# BoundedMultilinearOperators(X,Y),
      Zero_(BoundedMultilinearOperators(X,Y),
        R_VectorSpace_of_MultilinearOperators(X,Y)),
      Add_(BoundedMultilinearOperators(X,Y),
        R_VectorSpace_of_MultilinearOperators(X,Y)),
      Mult_(BoundedMultilinearOperators(X,Y),
        R_VectorSpace_of_MultilinearOperators(X,Y)) #) is RealLinearSpace;
    hence thesis by Th38,RSSPACE3:2;
  end;
