Quasi-compact operator, pseudo-essential spectra and some perturbation results

In this paper, we use the concept of quasi-compact operators, as a generalization of the class of Riesz operators, to improve the definition of the pseudo-Schechter essential spectrum of a closed densely defined operator acting on Banach space. Moreover, we discuss the incidence of some perturbation results on the behavior of pseudo-essential spectra of the sum of two bounded linear operators.