Scholarlink

<p>One of the popular generalizations of the classical notion of essential spectra is the notion of pseudo essential spectra. The study around such notion has gained intensive interest in many research fields, particularly, in the theory of Fredholm operators. So, the novelty of our work is to develop a new sufficient criteria linked to the notion of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_743_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Φ</mi> </math></EquationSource> <EquationSource Format="TEX">$\Phi $</EquationSource> </InlineEquation>-perturbation function (recently invested by M. Mebekhta in (J. Oper. Theory 51:3–18, <CitationRef CitationID="CR14">2004</CitationRef>)) allowing us to derive some new spectral analysis of some sets of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_743_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> <EquationSource Format="TEX">$\varepsilon $</EquationSource> </InlineEquation>-pseudo Fredholm operators and their corresponding pseudo Weyl essential spectra. Moreover, our aim comes also to reach a new characterization in the setting of the so-called pseudo Weyl essential spectrum of a closed densely defined operator via the above approach of perturbation. Our results in this paper generalize and refine earlier work, particularly, the work done by S. Charfi et al. (Indag. Math. 28(3):670–679, <CitationRef CitationID="CR7">2017</CitationRef>).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Insights into Some Sets of \(\varepsilon \)-Pseudo Fredholm Operators

  • 期刊论文

  • 发表日期：

    2025年9月8日

查看全文
  • Naila Bouida,
  • Ines Walha

摘要

One of the popular generalizations of the classical notion of essential spectra is the notion of pseudo essential spectra. The study around such notion has gained intensive interest in many research fields, particularly, in the theory of Fredholm operators. So, the novelty of our work is to develop a new sufficient criteria linked to the notion of Φ $\Phi $ -perturbation function (recently invested by M. Mebekhta in (J. Oper. Theory 51:3–18, 2004)) allowing us to derive some new spectral analysis of some sets of ε $\varepsilon $ -pseudo Fredholm operators and their corresponding pseudo Weyl essential spectra. Moreover, our aim comes also to reach a new characterization in the setting of the so-called pseudo Weyl essential spectrum of a closed densely defined operator via the above approach of perturbation. Our results in this paper generalize and refine earlier work, particularly, the work done by S. Charfi et al. (Indag. Math. 28(3):670–679, 2017).