Stability of relative essential spectra involving relative demicompactness concept in Banach algebra

Abstract

In this paper, we introduce and investigate a new concept that we call relative demicompact elements in Banach algebra as a generalization of relative
demicompact linear operators acting on Banach spaces. Our concept is used to
construct a new class of Fredholm perturbation with respect to a given Banach
subalgebra B, that contains its inessential ideal k_B and the set of left Fredholm
perturbations introduced in [6]. We show that it is a two-sided closed ideal of B
playing an important role in the characterization of the weyl spectrum of elements
affiliated with B.