{"title":"Unitary similarity and the numerical radius preservers","authors":"Abdellatif Bourhim , Mohamed Mabrouk","doi":"10.1016/j.laa.2025.03.005","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> be the algebra of all bounded linear operators acting on a separable infinite-dimensional complex Hilbert space <span><math><mi>H</mi></math></span>, and denote by <span><math><mi>w</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> the numerical radius of any operator <span><math><mi>T</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>. In this paper, we describe the form of all bijective linear maps <em>ϕ</em> on <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> for which <span><math><mi>w</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>)</mo><mo>=</mo><mi>w</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>)</mo></math></span> whenever <span><math><mi>T</mi><mo>,</mo><mspace></mspace><mi>S</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> are two unitarily similar operators.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"714 ","pages":"Pages 15-27"},"PeriodicalIF":1.1000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525001053","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let be the algebra of all bounded linear operators acting on a separable infinite-dimensional complex Hilbert space , and denote by the numerical radius of any operator . In this paper, we describe the form of all bijective linear maps ϕ on for which whenever are two unitarily similar operators.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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