{"title":"Geometric property (T) and Kazhdan projections","authors":"I. Vergara","doi":"10.1112/blms.13111","DOIUrl":null,"url":null,"abstract":"<p>We characterise Geometric Property (T) by the existence of a certain projection in the maximal uniform Roe algebra <span></span><math>\n <semantics>\n <mrow>\n <msubsup>\n <mi>C</mi>\n <mrow>\n <mi>u</mi>\n <mo>,</mo>\n <mi>max</mi>\n </mrow>\n <mo>∗</mo>\n </msubsup>\n <mrow>\n <mo>(</mo>\n <mi>X</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$C_{u,\\max }^*(X)$</annotation>\n </semantics></math>, extending the notion of Kazhdan projection for groups to the realm of metric spaces. We also describe this projection in terms of the decomposition of the metric space into coarsely connected components.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 9","pages":"2935-2950"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13111","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
Abstract
We characterise Geometric Property (T) by the existence of a certain projection in the maximal uniform Roe algebra , extending the notion of Kazhdan projection for groups to the realm of metric spaces. We also describe this projection in terms of the decomposition of the metric space into coarsely connected components.
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