Spectral Analysis of Perturbed Fredholm Operators

被引:0
|
作者
Sana Bouzidi
Nedra Moalla
Ines Walha
机构
[1] University of Sfax,Department of Mathematics
[2] Faculty of Sciences of Sfax,undefined
来源
Complex Analysis and Operator Theory | 2022年 / 16卷
关键词
Semi Fredholm operators; Fredholm operators; Compact operator; -perturbation function; Weyl spectrum; 47A10; 47A53; 34K08; 47A55;
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摘要
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.
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