Additive maps preserving semi-Fredholm operators with bounded ascent on $\mathcal B(\mathcal X)$

Abstract

Let X be an infinite-dimensional complex Banach space, and B(X) the algebra of all bounded linear operators on X. In this paper, given any positive integer m, we characterize the surjective additive maps on B(X) that preserve semi-Fredholm operators with ascent non-greater than m in both directions, and describe completely the structure of these maps.