Generalized Relative Essential Spectra

Abstract

The aim of the present paper is to give some spectral results about generalized
Fredholm operators and the so called S-generalized Fredholm operators, where S is a
given bounded linear operator acting on a Banach space X. When X possesses some
properties, we provide then some sufficient conditions for which a bounded linear operator
will be a generalized Fredholm. The obtained results are applied to characterize the so
called generalized S-essential spectrum, in particular the S-Jeribi essential spectrum [15].
These results are formulated in terms of measure of weak noncompactness