{"title":"Banach代数的一些上同调性质","authors":"M. Shams, K. Azar","doi":"10.30495/JME.V0I0.1395","DOIUrl":null,"url":null,"abstract":"In this manuscript, we investigate and study some cohomological properties of Banach algebras. Let $A$ be a Banach algebra with left bounded approximate identity, and let $B$ be a Banach $A-bimodule$. We show that if $AB^{**}$ and $B^{**}A$ are subset of $B$, then $H^1(A,B^{(2n+1)})=0$ for all $n\\geq 0$, whenever $H^1(A,B^*)=0$.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some cohomological properties of Banach algebras\",\"authors\":\"M. Shams, K. Azar\",\"doi\":\"10.30495/JME.V0I0.1395\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this manuscript, we investigate and study some cohomological properties of Banach algebras. Let $A$ be a Banach algebra with left bounded approximate identity, and let $B$ be a Banach $A-bimodule$. We show that if $AB^{**}$ and $B^{**}A$ are subset of $B$, then $H^1(A,B^{(2n+1)})=0$ for all $n\\\\geq 0$, whenever $H^1(A,B^*)=0$.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.1395\",\"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":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1395","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this manuscript, we investigate and study some cohomological properties of Banach algebras. Let $A$ be a Banach algebra with left bounded approximate identity, and let $B$ be a Banach $A-bimodule$. We show that if $AB^{**}$ and $B^{**}A$ are subset of $B$, then $H^1(A,B^{(2n+1)})=0$ for all $n\geq 0$, whenever $H^1(A,B^*)=0$.
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