{"title":"Inheritance of certain comparison and divisibility properties for generalized tracially approximated C*-algebras","authors":"Xiaochun Fang, Zhongli Wang","doi":"10.1007/s43034-024-00399-w","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\(\\Omega \\)</span> be a class of C*-algebras with the <i>m</i>-comparison property (respectively, the <i>n</i>-almost divisibility property, the weakly (<i>k</i>, <i>n</i>)-divisibility property). We show that any infinite-dimensional simple unital C*-algebra in the class GTA<span>\\(\\Omega \\)</span> (the class of C*-algebras which can be generalized tracially approximated by the C*-algebras in <span>\\(\\Omega \\)</span>) has <i>m</i>-comparison (respectively, is <span>\\((2n+1)\\)</span>-almost divisible, is weakly (<i>k</i>, 2<i>n</i>)-divisible).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-024-00399-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(\Omega \) be a class of C*-algebras with the m-comparison property (respectively, the n-almost divisibility property, the weakly (k, n)-divisibility property). We show that any infinite-dimensional simple unital C*-algebra in the class GTA\(\Omega \) (the class of C*-algebras which can be generalized tracially approximated by the C*-algebras in \(\Omega \)) has m-comparison (respectively, is \((2n+1)\)-almost divisible, is weakly (k, 2n)-divisible).
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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