Spectral Analysis of Perturbed Fredholm Operators

In this proposed paper, we use a newly introduced perturbation concept in the literature originated by M. Mbekhta in J. Oper. Theo. 51, 3–18, 2004), which is the Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi $$\end{document}-perturbation function, allowing to derive an original stability results intervening in the theory of perturbed Fredholm operators. Our results are subsequently used to investigate a new characterization of Weyl spectrum of linear operator under such concept of Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi $$\end{document}-perturbation function. The last part is devoted to study the problem of the stability of perturbed semi-Fredholm operators via this kind of function approach. The theoretical results are illustrated by some examples.