{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000300","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
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].
$L^1(G)$ is always weakly amenable [10].
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