{"title":"关于超环/超环算子的谱","authors":"Pietro Aiena, Fabio Burderi, Salvatore Triolo","doi":"10.1007/s43036-025-00437-x","DOIUrl":null,"url":null,"abstract":"<div><p>This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators <i>T</i> in the case were the dual <span>\\(T^*\\)</span> has empty point spectrum.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00437-x.pdf","citationCount":"0","resultStr":"{\"title\":\"On the spectrum of supercyclic/hypercyclic operators\",\"authors\":\"Pietro Aiena, Fabio Burderi, Salvatore Triolo\",\"doi\":\"10.1007/s43036-025-00437-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators <i>T</i> in the case were the dual <span>\\\\(T^*\\\\)</span> has empty point spectrum.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 3\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-025-00437-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-025-00437-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00437-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the spectrum of supercyclic/hypercyclic operators
This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators T in the case were the dual \(T^*\) has empty point spectrum.
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