On the Pseudo Semi-Browder Essential Spectra and Application to 2 \times 2 Block Operator Matrices

Abstract

In the present paper, we introduce and study the pseudo semi-Browder essential spectra of bounded linear operators in a Banach space.We start by dening the pseudo semi-Browder operators and we prove the stability of these operators under commuting Riesz operator perturbations.
Then, we apply the obtained results to study the stability of the pseudo semi-Browder essential spectra. We show as well the relation between the pseudo semi-Browder spectra of the sum of two bounded linear operators and the pseudo semi-Browder spectrum of each of these operators. As an application, we study the pseudo semi-Browder spectra of 2 \times 2 block operator matrices.

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