{"title":"实际功率的数值半径和几何平均数","authors":"Yuki Seo","doi":"10.1007/s43036-024-00328-7","DOIUrl":null,"url":null,"abstract":"<div><p>Norm inequalities related to geometric means are discussed by many researchers. Though the operator norm is unitarily invariant one, the numerical radius is not so and unitarily similar. In this paper, we prove some numerical radius inequalities that are related to operator geometric means and spectral geometric ones of real power for positive invertible operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical radius and geometric means of real power\",\"authors\":\"Yuki Seo\",\"doi\":\"10.1007/s43036-024-00328-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Norm inequalities related to geometric means are discussed by many researchers. Though the operator norm is unitarily invariant one, the numerical radius is not so and unitarily similar. In this paper, we prove some numerical radius inequalities that are related to operator geometric means and spectral geometric ones of real power for positive invertible operators.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00328-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00328-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Numerical radius and geometric means of real power
Norm inequalities related to geometric means are discussed by many researchers. Though the operator norm is unitarily invariant one, the numerical radius is not so and unitarily similar. In this paper, we prove some numerical radius inequalities that are related to operator geometric means and spectral geometric ones of real power for positive invertible operators.
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