{"title":"半简单Banach代数中的广义Drazin-Riesz可逆元","authors":"Othman Abad, Hassane Zguitti","doi":"10.1007/s13370-024-01227-z","DOIUrl":null,"url":null,"abstract":"<div><p>We extend the notion of generalized Drazin-Riesz inverse introduced for bounded linear operators in Živković-Zlatanović and Cvetković (Linear Multilinear Algebra 65(6):1171–1193, 2017) to elements in a complex unital semi-simple Banach algebra. Several characterizations and properties of generalized Drazin-Riesz invertible elements are given. In particular, we extend those of Abad and Zguitti (Ann Funct Anal 12:Article number: 55, 2021), Djordjević and Stanimirovic (Czech Math J 51(3):617–634, 2001) and Živković-Zlatanović and Cvetković (2017).</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Drazin-Riesz invertible elements in a semi-simple Banach algebra\",\"authors\":\"Othman Abad, Hassane Zguitti\",\"doi\":\"10.1007/s13370-024-01227-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We extend the notion of generalized Drazin-Riesz inverse introduced for bounded linear operators in Živković-Zlatanović and Cvetković (Linear Multilinear Algebra 65(6):1171–1193, 2017) to elements in a complex unital semi-simple Banach algebra. Several characterizations and properties of generalized Drazin-Riesz invertible elements are given. In particular, we extend those of Abad and Zguitti (Ann Funct Anal 12:Article number: 55, 2021), Djordjević and Stanimirovic (Czech Math J 51(3):617–634, 2001) and Živković-Zlatanović and Cvetković (2017).</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01227-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01227-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generalized Drazin-Riesz invertible elements in a semi-simple Banach algebra
We extend the notion of generalized Drazin-Riesz inverse introduced for bounded linear operators in Živković-Zlatanović and Cvetković (Linear Multilinear Algebra 65(6):1171–1193, 2017) to elements in a complex unital semi-simple Banach algebra. Several characterizations and properties of generalized Drazin-Riesz invertible elements are given. In particular, we extend those of Abad and Zguitti (Ann Funct Anal 12:Article number: 55, 2021), Djordjević and Stanimirovic (Czech Math J 51(3):617–634, 2001) and Živković-Zlatanović and Cvetković (2017).
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