{"title":"有限von Neumann代数上的酉不变范数","authors":"Haihui Fan, Don Hadwin","doi":"10.1007/s44146-023-00075-w","DOIUrl":null,"url":null,"abstract":"<div><p>We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The characterization is analogous to von Neumann’s characterization for the <span>\\(n\\times n\\)</span> complex matrices and the characterization in Fang et al. (J Funct Anal 255(1):142–183, 2008) for <span>\\(II_{1}\\)</span> factors.\n</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"449 - 499"},"PeriodicalIF":0.5000,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unitarily invariant norms on finite von Neumann algebras\",\"authors\":\"Haihui Fan, Don Hadwin\",\"doi\":\"10.1007/s44146-023-00075-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The characterization is analogous to von Neumann’s characterization for the <span>\\\\(n\\\\times n\\\\)</span> complex matrices and the characterization in Fang et al. (J Funct Anal 255(1):142–183, 2008) for <span>\\\\(II_{1}\\\\)</span> factors.\\n</p></div>\",\"PeriodicalId\":46939,\"journal\":{\"name\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"volume\":\"89 3-4\",\"pages\":\"449 - 499\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s44146-023-00075-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/s44146-023-00075-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unitarily invariant norms on finite von Neumann algebras
We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The characterization is analogous to von Neumann’s characterization for the \(n\times n\) complex matrices and the characterization in Fang et al. (J Funct Anal 255(1):142–183, 2008) for \(II_{1}\) factors.
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