theorem Th20:
  for X,Y be ComplexNormSpace holds for f be LinearOperator of X,Y
  st (for x be VECTOR of X holds f.x=0.Y) holds f is Lipschitzian
proof
  let X,Y be ComplexNormSpace;
  let f be LinearOperator of X,Y such that
A1: for x be VECTOR of X holds f.x=0.Y;
A2: now
    let x be VECTOR of X;
    thus ||. f.x .|| = ||. 0.Y .|| by A1
      .=0*||. x .|| by CLVECT_1:102;
  end;
  take 0;
  thus thesis by A2;
end;
