Additive Drazin inverse preservers

Let H be a real or complex Hilbert space and B(H) denote the Banach algebra of all bounded linear operators on H. For T epsilon B(H), if there exists an operator T-D epsilon B(H) and a positive integer k such that TTD=(TT)-T-D, (TTTD)-T-D=T-D, (Tk+1TD)=T-k, then T is said to be Drazin invertible, and T-D is a Drazin inverse of T. We say a map Phi : B(H) -> B(H) preserves Drazin inverse if Phi(T-D) = Phi(T)(D) for every Drazin invertible operator T epsilon B(H). In this paper, we determine the structures of additive maps on B(H) preserving Drazin inverses. (c) 2007 Elsevier Inc. All rights reserved.