
theorem Th26:
  for X, Y, Z be RealNormSpace holds
  0.R_VectorSpace_of_BoundedBilinearOperators(X,Y,Z)
  = (the carrier of [:X,Y:]) --> 0.Z
  proof
    let X, Y, Z be RealNormSpace;
    A1: 0.R_VectorSpace_of_BilinearOperators(X,Y,Z)
      = ((the carrier of [:X,Y:]) -->0.Z) by Th18;
    R_VectorSpace_of_BoundedBilinearOperators(X,Y,Z)
      is Subspace of R_VectorSpace_of_BilinearOperators(X,Y,Z) by RSSPACE:11;
    hence thesis by A1,RLSUB_1:11;
  end;
