Stability analysis of some types of pseudo essential spectra under quasi compact perturbations

The notion of pseudo essential spectra appears as one of famous generalization of the classical notion of essential spectra. In this paper, we analysis the stability result of perturbed pseudo upper (lower)-Fredholm, pseudo upper (lower)-Weyl and pseudo upper (lower)-Browder operators by means of quasi compact criterions of perturbation. We show some pseudo essential spectra relations between these kind of operators. In addition, a new characterization of the sum of two linear bounded operators in Banach spaces is invested in terms of some essential pseudo spectra based on sufficient criterion of quasi compact perturbation.