{"title":"Browder S-Resolvent Equation in Quaternionic Setting","authors":"Hatem Baloudi, Aref Jeribi, Habib Zmouli","doi":"10.1007/s11785-024-01515-3","DOIUrl":null,"url":null,"abstract":"<p>This paper is devoted to the study of the <i>S</i>-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the <i>S</i>-spectrum. Furthermore, we introduce the left and right Browder <i>S</i>-resolvent operators. Inspired by the <i>S</i>-resolvent equation, we give the Browder’s <i>S</i>-resolvent equation in quaternionic setting.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01515-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to the study of the S-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S-spectrum. Furthermore, we introduce the left and right Browder S-resolvent operators. Inspired by the S-resolvent equation, we give the Browder’s S-resolvent equation in quaternionic setting.
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