{"title":"Recurrency on the Space of Hilbert-Schmidt Operators","authors":"Mansooreh Moosapoor","doi":"10.21123/bsj.2023.8870","DOIUrl":null,"url":null,"abstract":"In this paper, it is proved that if a C0-semigroup is chaotic, hypermixing or supermixing, then the related left multiplication C0-semigroup on the space of Hilbert-Schmidt operators is recurrent if and only if it is hypercyclic. Also, it is stated that under some conditions recurrence of a C0-semigroup and the recurrency of the left multiplication C0-semigroup that is related to it, on the space of Hilbert-Schmidt operators are equivalent. Moreover, some sufficient conditions for recurrency and hypercyclicity of the left multiplication C0-semigroup are presented that are based on dense subsets","PeriodicalId":8687,"journal":{"name":"Baghdad Science Journal","volume":"54 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Baghdad Science Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21123/bsj.2023.8870","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, it is proved that if a C0-semigroup is chaotic, hypermixing or supermixing, then the related left multiplication C0-semigroup on the space of Hilbert-Schmidt operators is recurrent if and only if it is hypercyclic. Also, it is stated that under some conditions recurrence of a C0-semigroup and the recurrency of the left multiplication C0-semigroup that is related to it, on the space of Hilbert-Schmidt operators are equivalent. Moreover, some sufficient conditions for recurrency and hypercyclicity of the left multiplication C0-semigroup are presented that are based on dense subsets
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