{"title":"函数微积分下\\（｛\\cal A｝｛\\cl N｝\\）-算子的稳定性","authors":"G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki","doi":"10.1007/s10476-023-0231-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this note we discuss absolutely norm attaining property (<span>\\({\\cal A}{\\cal N}\\)</span>-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the <span>\\({\\cal A}{\\cal N}\\)</span>-property under the functional calculus. As a consequence we discuss the operator mean of positive <span>\\({\\cal A}{\\cal N}\\)</span>-operators.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0231-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Stability of \\\\({\\\\cal A}{\\\\cal N}\\\\)-Operators under Functional Calculus\",\"authors\":\"G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki\",\"doi\":\"10.1007/s10476-023-0231-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note we discuss absolutely norm attaining property (<span>\\\\({\\\\cal A}{\\\\cal N}\\\\)</span>-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the <span>\\\\({\\\\cal A}{\\\\cal N}\\\\)</span>-property under the functional calculus. As a consequence we discuss the operator mean of positive <span>\\\\({\\\\cal A}{\\\\cal N}\\\\)</span>-operators.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10476-023-0231-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0231-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0231-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability of \({\cal A}{\cal N}\)-Operators under Functional Calculus
In this note we discuss absolutely norm attaining property (\({\cal A}{\cal N}\)-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the \({\cal A}{\cal N}\)-property under the functional calculus. As a consequence we discuss the operator mean of positive \({\cal A}{\cal N}\)-operators.
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