{"title":"Insights into a new class of unbounded operators","authors":"Aymen Bahloul","doi":"10.1515/gmj-2024-2047","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to introduce the new class of left and right B-Weyl operators, which naturally extends the conventional concepts of left and right Weyl operators. Our contributions encompass demonstrating the stability of the left (and right) B-Weyl operators under small perturbations. We further characterize the left (and right) B-Weyl operators as the direct sum of a closed left (and right) Drazin invertible operator and a finite rank operator. Additionally, we present some characterizations of the left and right B-Weyl spectra, utilizing the left and right Drazin spectra as essential components. Furthermore, our obtained results play a pivotal role in exploring the interrelations between the left and right B-Weyl spectra and other spectra integral to the realm of B-Fredholm theory. This paper seeks to enhance and extend the recent research explored in [F. Abdmouleh and T. Ben Lakhal, Left and right B-Fredholm operators, Ukrainian Math. J. 74 2023, 10, 1479–1489] to a larger class in the unbounded B-Fredholm operators theory.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2047","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to introduce the new class of left and right B-Weyl operators, which naturally extends the conventional concepts of left and right Weyl operators. Our contributions encompass demonstrating the stability of the left (and right) B-Weyl operators under small perturbations. We further characterize the left (and right) B-Weyl operators as the direct sum of a closed left (and right) Drazin invertible operator and a finite rank operator. Additionally, we present some characterizations of the left and right B-Weyl spectra, utilizing the left and right Drazin spectra as essential components. Furthermore, our obtained results play a pivotal role in exploring the interrelations between the left and right B-Weyl spectra and other spectra integral to the realm of B-Fredholm theory. This paper seeks to enhance and extend the recent research explored in [F. Abdmouleh and T. Ben Lakhal, Left and right B-Fredholm operators, Ukrainian Math. J. 74 2023, 10, 1479–1489] to a larger class in the unbounded B-Fredholm operators theory.
本文旨在介绍左、右 B-韦尔算子这一新类别，它自然地扩展了左、右韦尔算子的传统概念。我们的贡献包括证明左（和右）B-Weyl 算子在微小扰动下的稳定性。我们进一步将左（和右）B-Weyl 算子描述为封闭的左（和右）Drazin 不可逆算子与有限秩算子的直接和。此外，我们还利用左、右德拉津谱作为基本组成部分，提出了左、右 B-Weyl 谱的一些特征。此外，我们所获得的结果对于探索左、右 B-Weyl 光谱与 B-Fredholm 理论领域中其他光谱之间的相互关系起到了关键作用。本文试图加强和扩展最近在 [F. Abdmouleh and T. Abdmouleh and T. Abdmouleh and T. Abdmouleh] 中探索的研究。Abdmouleh 和 T. Ben Lakhal, 左和右 B-Fredholm 算子, 乌克兰数学.J. 74 2023, 10, 1479-1489] 中探索的无界 B-Fredholm 算子理论的更大范畴。
期刊介绍：
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.
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