Spectral description of Fredholm operators via polynomially Riesz operators perturbation

Abstract

Abstract In this paper, we establish some spectral analysis in Fredholm theory involving the concept of a polynomially Riesz operators perturbation. Moreover, we apply the obtained results to analyze the incidence of some essential spectra of a perturbed operator via this kind of perturbation. Our approach allows us to investigate a new description in the theory of unbounded operator matrices defined with maximal domain via this kind of perturbation. Finally, we conclude by presenting some progress in the theory of polynomially operators and the theory of semi-Fredholm and semi-Browder operators.