{"title":"Common spectral properties and $$\\nu $$ -convergence","authors":"Soufiane Hadji, Hassane Zguitti","doi":"10.1007/s43037-024-00350-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper we show that if <span>\\(\\{T_n\\}\\)</span> is a sequence of bounded linear operators on a complex Banach space <i>X</i> which <span>\\(\\nu \\)</span>-converges to two different bounded linear operators <i>T</i> and <i>U</i>, then <i>T</i> and <i>U</i> have the same parts of the spectrum. In particular, we generalize the results of Sánchez-Perales and Djordjević (J Math Anal Appl 433:405–415, 2016) and of Ammar (Indag Math 28:424–435, 2017). We also investigate the spectral <span>\\(\\nu \\)</span>-continuity for the surjective spectrum.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Banach Journal of Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s43037-024-00350-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we show that if \(\{T_n\}\) is a sequence of bounded linear operators on a complex Banach space X which \(\nu \)-converges to two different bounded linear operators T and U, then T and U have the same parts of the spectrum. In particular, we generalize the results of Sánchez-Perales and Djordjević (J Math Anal Appl 433:405–415, 2016) and of Ammar (Indag Math 28:424–435, 2017). We also investigate the spectral \(\nu \)-continuity for the surjective spectrum.
期刊介绍：
The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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