{"title":"On Subspace-recurrent Operators","authors":"M. Moosapoor","doi":"10.5556/J.TKJM.53.2022.3579","DOIUrl":null,"url":null,"abstract":"In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if T is an invertible chaotic or an invertible subspace-chaotic operator, then T, T−n and λT are subspace-recurrent for any positive integer n and any scalar λ with absolute value 1. Also, we state a subspace-recurrence criterion.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/J.TKJM.53.2022.3579","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if T is an invertible chaotic or an invertible subspace-chaotic operator, then T, T−n and λT are subspace-recurrent for any positive integer n and any scalar λ with absolute value 1. Also, we state a subspace-recurrence criterion.
期刊介绍：
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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