{"title":"算子值自由卷积的原子","authors":"S. Belinschi, H. Bercovici, Weihua Liu","doi":"10.7900/jot.2019dec07.2283","DOIUrl":null,"url":null,"abstract":"Suppose that X1 and X2 are two selfadjoint random variables that are freely independent over an operator algebra B. We describe the possible operator atoms of the distribution of X1+X2 and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial p(X1,X2) in case B=C.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The atoms of operator-valued free convolutions\",\"authors\":\"S. Belinschi, H. Bercovici, Weihua Liu\",\"doi\":\"10.7900/jot.2019dec07.2283\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Suppose that X1 and X2 are two selfadjoint random variables that are freely independent over an operator algebra B. We describe the possible operator atoms of the distribution of X1+X2 and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial p(X1,X2) in case B=C.\",\"PeriodicalId\":50104,\"journal\":{\"name\":\"Journal of Operator Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7900/jot.2019dec07.2283\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/jot.2019dec07.2283","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Suppose that X1 and X2 are two selfadjoint random variables that are freely independent over an operator algebra B. We describe the possible operator atoms of the distribution of X1+X2 and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial p(X1,X2) in case B=C.
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The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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