{"title":"On integral extensions of Banach algebras","authors":"Sara El Kinani, Rachid Choukri","doi":"10.1007/s44146-023-00091-w","DOIUrl":null,"url":null,"abstract":"<div><p>We consider countable extensions of commutative and unital Banach algebras. We study these Banach algebra structures with or without assuming the continuity of the canonical injection. We also prove that a countable extension endowed with a Banach algebra norm with continuous injection is actually a finite extension.\n</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"501 - 508"},"PeriodicalIF":0.5000,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-023-00091-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider countable extensions of commutative and unital Banach algebras. We study these Banach algebra structures with or without assuming the continuity of the canonical injection. We also prove that a countable extension endowed with a Banach algebra norm with continuous injection is actually a finite extension.
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