{"title":"C*-代数的一个改进相似度","authors":"Don Hadwin, Junhao Shen","doi":"10.1007/s44146-022-00043-w","DOIUrl":null,"url":null,"abstract":"<div><p>We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove\nthat if every <i>II</i><sub>1</sub> factor representation of a separable C*-algebra <span>\\(\\mathcal{A}\\)</span> has\nproperty <span>\\(\\Gamma\\)</span>, then the similarity degree of <span>\\(\\mathcal{A}\\)</span> is at most 11.\n</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"88 3-4","pages":"627 - 637"},"PeriodicalIF":0.5000,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A modified similarity degree for C*-algebras\",\"authors\":\"Don Hadwin, Junhao Shen\",\"doi\":\"10.1007/s44146-022-00043-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove\\nthat if every <i>II</i><sub>1</sub> factor representation of a separable C*-algebra <span>\\\\(\\\\mathcal{A}\\\\)</span> has\\nproperty <span>\\\\(\\\\Gamma\\\\)</span>, then the similarity degree of <span>\\\\(\\\\mathcal{A}\\\\)</span> is at most 11.\\n</p></div>\",\"PeriodicalId\":46939,\"journal\":{\"name\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"volume\":\"88 3-4\",\"pages\":\"627 - 637\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s44146-022-00043-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-022-00043-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove
that if every II1 factor representation of a separable C*-algebra \(\mathcal{A}\) has
property \(\Gamma\), then the similarity degree of \(\mathcal{A}\) is at most 11.
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