{"title":"ON OPERATORS WHICH ARE POWER SIMILAR TO HYPONORMAL OPERATORS","authors":"Sungeun Jung, E. Ko, Mee-Jung Lee","doi":"10.18910/57659","DOIUrl":null,"url":null,"abstract":"In this paper, we study power similarity of operators. In particular, we show that if $T \\in \\mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T \\in \\mathit{PS}(H)$.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Osaka Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18910/57659","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we study power similarity of operators. In particular, we show that if $T \in \mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T \in \mathit{PS}(H)$.
期刊介绍：
Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.
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