Pseudo Essential Spectra in Banach Space and Application to Operator Matrices

In this paper, we introduce and study the pseudo left (right)-Fredholm and pseudo left (right)-Browder essential spectra of bounded linear operators in a Banach space. We start by giving the definition and we investigate some proprieties of these pseudo essential spectra like the stability under Riesz operator perturbations. Moreover, we describe the pseudo left (right)-Fredholm and pseudo left (right)-Browder essential spectra of the sum of two bounded linear operators. Finally, we apply the obtained result to characterize the pseudo left (right)-Fredholm and pseudo left (right)-Browder spectra of 2x2 block operator matrices.