{"title":"具有连续导数的素数Banach代数","authors":"Mohamed Moumen, L. Taoufiq, A. Boua","doi":"10.24193/mathcluj.2023.1.13","DOIUrl":null,"url":null,"abstract":"Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On prime Banach algebras with continuous derivations\",\"authors\":\"Mohamed Moumen, L. Taoufiq, A. Boua\",\"doi\":\"10.24193/mathcluj.2023.1.13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/mathcluj.2023.1.13\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2023.1.13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
On prime Banach algebras with continuous derivations
Let A be a Banach algebra over R or C with center Z(A). In this paper, we show that, if a non-injective continuous derivation of A satisfies some local differential identities, then A must be commutative. We give several applications, and we provide examples to show that some hypotheses of our theorems are necessary.
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