Nonlinear maps preserving semi-Fredholm operators with bounded nullity

Abstract

Let X be an infinite dimensional complex Banach space, and let B(X) be the algebra of all bounded linear operators on X. In this paper, given any positive integer n, we provide a characterization of all bijective maps on B(X) preserving the difference of semi-Fredholm operators with nullity less than n, and describe completely the structure of these maps.