
theorem Th26:
  for X being RealNormSpace-Sequence,
      Y be RealNormSpace
  holds
    0.R_VectorSpace_of_BoundedMultilinearOperators(X,Y)
    = (the carrier of product X) --> 0.Y
  proof
    let X be RealNormSpace-Sequence,
        Y be RealNormSpace;
    A1: 0.R_VectorSpace_of_MultilinearOperators(X,Y)
      = ((the carrier of product X) --> 0.Y) by Th18;
    R_VectorSpace_of_BoundedMultilinearOperators(X,Y) is Subspace of
      R_VectorSpace_of_MultilinearOperators(X,Y) by RSSPACE:11;
    hence thesis by A1,RLSUB_1:11;
  end;
