{"title":"对偶巴拿赫代数的弱可配性","authors":"Amin Mahmoodi","doi":"10.1017/s0013091524000300","DOIUrl":null,"url":null,"abstract":"<p>A suitable notion of weak amenability for dual Banach algebras, which we call weak Connes amenability, is defined and studied. Among other things, it is proved that the measure algebra <span>M</span>(<span>G</span>) of a locally compact group <span>G</span> is always weakly Connes amenable. It can be a complement to Johnson’s theorem that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240426094551681-0933:S0013091524000300:S0013091524000300_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$L^1(G)$</span></span></img></span></span> is always weakly amenable [10].</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak amenability for dual Banach algebras\",\"authors\":\"Amin Mahmoodi\",\"doi\":\"10.1017/s0013091524000300\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A suitable notion of weak amenability for dual Banach algebras, which we call weak Connes amenability, is defined and studied. Among other things, it is proved that the measure algebra <span>M</span>(<span>G</span>) of a locally compact group <span>G</span> is always weakly Connes amenable. It can be a complement to Johnson’s theorem that <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240426094551681-0933:S0013091524000300:S0013091524000300_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$L^1(G)$</span></span></img></span></span> is always weakly amenable [10].</p>\",\"PeriodicalId\":20586,\"journal\":{\"name\":\"Proceedings of the Edinburgh Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Edinburgh Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0013091524000300\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Edinburgh Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000300","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们定义并研究了对偶巴拿赫代数的一个合适的弱可亲和性概念，我们称之为弱康恩可亲和性。除其他外，我们还证明了局部紧凑群 G 的度量代数 M(G) 总是弱康恩可亲和性的。它可以作为约翰逊关于 $L^1(G)$ 总是弱可朋性定理的补充[10]。
A suitable notion of weak amenability for dual Banach algebras, which we call weak Connes amenability, is defined and studied. Among other things, it is proved that the measure algebra M(G) of a locally compact group G is always weakly Connes amenable. It can be a complement to Johnson’s theorem that $L^1(G)$ is always weakly amenable [10].
期刊介绍：
The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.
$L^1(G)$ is always weakly amenable [10].
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