Generalized essential spectra involving the class of g-g-Riesz operators

In this paper, we explore the spectral properties of unbounded generalized Fredholm operators acting on a non-reflexive Banach space X. The results are formulated in terms of some topological conditions made on X or on its dual X * {X^{*}} . In addition, we introduce the concept of the so-called g-g-Riesz linear operators as an extension of Riesz operators. The obtained results are used to discuss the incidence of the behavior of generalized essential spectra. Furthermore, a relation between the generalized essential spectrum and the left (resp. the right) essential spectrum by means of g-Riesz perturbation is provided.