Additive Drazin inverse preservers Original Research Article

Let H be a real or complex Hilbert space and image denote the Banach algebra of all bounded linear operators on H. For image, if there exists an operator image and a positive integer k such thatimagethen T is said to be Drazin invertible, and TD is a Drazin inverse of T. We say a map image preserves Drazin inverse if Φ(TD)=Φ(T)D for every Drazin invertible operator image. In this paper, we determine the structures of additive maps on image preserving Drazin inverses.