Linear Maps Preserving the Spectral Radius

LetXbe a complex Banach space. IfΦ: B(X)→B(X) is a surjective linear map such thatAandΦ(A) have the same spectral radius for everyA∈B(X), thenΦ=cΘwhereΘis either an algebra-automorphism or an antiautomorphism of B(X) andcis a complex constant such that |c|=1.