{"title":"Remark on square roots of self-adjoint weighted composition operators on H2","authors":"Sungeun Jung , Yoenha Kim , Eungil Ko","doi":"10.1016/j.jmaa.2024.128970","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study square roots of self-adjoint weighted composition operators on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. More precisely, we focus on square roots <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> of a self-adjoint operator <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>g</mi><mo>,</mo><mi>ψ</mi></mrow></msub><mo>=</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> when <em>φ</em> is a linear fractional selfmap of <span><math><mi>D</mi></math></span>. We also investigate several properties of such <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span>. Finally, we show that the square roots <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> may be other, nonself-adjoint weighted composition operators and have nontrivial invariant subspaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128970"},"PeriodicalIF":1.2000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008928","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study square roots of self-adjoint weighted composition operators on . More precisely, we focus on square roots of a self-adjoint operator when φ is a linear fractional selfmap of . We also investigate several properties of such . Finally, we show that the square roots may be other, nonself-adjoint weighted composition operators and have nontrivial invariant subspaces.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.