Linear maps preserving the spectral radius

Let X be a complex Banach space. If Phi: B(X) --> B(X) is a surjective linear map such that A and Phi(A) have the same spectral radius for every A is an element of B(X), then Phi = c Theta where Theta is either an algebra-automorphism or antiautomorphism of B(X) and c is complex constant such that /c/ = 1. (C) 1996 Academic Press, Inc.