{"title":"对称算子均值","authors":"Mitsuru Uchiyama","doi":"10.1007/s44146-024-00141-x","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this paper is to extend symmetric means of multi-variable positive matrices to those of multi-variable positive operators on an infinite dimensional Hilbert space. We also consider the situations where symmetric means of operators <i>A</i>, <i>B</i>, <i>C</i> become linear combinations of them.\n</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"593 - 604"},"PeriodicalIF":0.5000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00141-x.pdf","citationCount":"0","resultStr":"{\"title\":\"Symmetric operator means\",\"authors\":\"Mitsuru Uchiyama\",\"doi\":\"10.1007/s44146-024-00141-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The purpose of this paper is to extend symmetric means of multi-variable positive matrices to those of multi-variable positive operators on an infinite dimensional Hilbert space. We also consider the situations where symmetric means of operators <i>A</i>, <i>B</i>, <i>C</i> become linear combinations of them.\\n</p></div>\",\"PeriodicalId\":46939,\"journal\":{\"name\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"volume\":\"90 3-4\",\"pages\":\"593 - 604\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s44146-024-00141-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s44146-024-00141-x\",\"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/s44146-024-00141-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The purpose of this paper is to extend symmetric means of multi-variable positive matrices to those of multi-variable positive operators on an infinite dimensional Hilbert space. We also consider the situations where symmetric means of operators A, B, C become linear combinations of them.
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