Index for generalized Fredholm operators and generalized perturbation theory

Abstract

Abstract In this paper, we develop some generalized Fredholm perturbation results for bounded linear operators acting on non-reflexive Banach spaces satisfying certain conditions. Furthermore, we investigate the stability of the generalized Schechter S-essential spectrum by means of the so-called generalized Fredholm index. This concept is introduced as a semigroup homomorphism satisfying certain properties. Some generalized Fredholm results for block operator matrices acting on a non-reflexive product of two Banach spaces are also developed.