
theorem Th23:
  for X,Y be RealNormSpace holds
  BoundedMultilinearOperators(<*X*>,Y)
    = BoundedLinearOperators(product <*X*>,Y)
  proof
    let X,Y be RealNormSpace;
    for f be object holds
    f in BoundedMultilinearOperators(<*X*>,Y)
    iff f in BoundedLinearOperators(product <*X*>,Y)
    proof
      let f be object;
      f is Lipschitzian LinearOperator of product <*X*>,Y
      iff f is Lipschitzian MultilinearOperator of <*X*>,Y
        by Th21;
      hence thesis by LOPBAN_1:def 9,LOPBAN10:def 11;
    end;
    hence thesis by TARSKI:2;
  end;
