On the characterization of the $\overline{\gamma}$-pseudo left-right Browder essential spectra of the sum of two bounded operators

Abstract

In this paper, we study the stability of the $\overline{\gamma}$-pseudo left and right Browder essential spectra of bounded linear operators on Banach spaces. Firstly, we introduce new classes of operators called $\overline{\gamma}$-pseudo left and right Browder operators. Moreover, we examine the invariance of their corresponding spectra sets under Riesz perturbations. Finally, we study the $\overline{\gamma}$-pseudo semi-Browder spectra of the sum of two bounded linear operators, exploring its relation with the pseudo semi-Browder spectrum of each of these operators.