{"title":"关于理想 C $$^*$$ -补全和可亲和性的说明","authors":"Tomasz Kochanek","doi":"10.1007/s00010-024-01077-x","DOIUrl":null,"url":null,"abstract":"<p>For a discrete group <i>G</i>, we consider certain ideals <span>\\(\\mathcal {I}\\subset c_0(G)\\)</span> of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C<span>\\(^*\\)</span>-algebra of <i>G</i> and the C<span>\\(^*\\)</span>-completion <span>\\(\\textrm{C}^*_{\\mathcal {I}}(G)\\)</span> in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that <i>G</i> is amenable.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on ideal C $$^*$$ -completions and amenability\",\"authors\":\"Tomasz Kochanek\",\"doi\":\"10.1007/s00010-024-01077-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For a discrete group <i>G</i>, we consider certain ideals <span>\\\\(\\\\mathcal {I}\\\\subset c_0(G)\\\\)</span> of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C<span>\\\\(^*\\\\)</span>-algebra of <i>G</i> and the C<span>\\\\(^*\\\\)</span>-completion <span>\\\\(\\\\textrm{C}^*_{\\\\mathcal {I}}(G)\\\\)</span> in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that <i>G</i> is amenable.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00010-024-01077-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00010-024-01077-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
对于离散群 G，我们考虑了某些序列的理想（(\mathcal {I}\subset c_0(G)\) of sequences with prescribed rate of convergence to zero）。我们证明，在布朗和根特纳（Bull. London Math. Soc. 45:1181-1193，2013）的意义上，G 的全群 C\(^*\)-algebra 与 C\(^*\)-completion \(\textrm{C}^*_{mathcal {I}}(G)\)之间的相等性意味着 G 是可封闭的。
A note on ideal C $$^*$$ -completions and amenability
For a discrete group G, we consider certain ideals \(\mathcal {I}\subset c_0(G)\) of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C\(^*\)-algebra of G and the C\(^*\)-completion \(\textrm{C}^*_{\mathcal {I}}(G)\) in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that G is amenable.
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