Quasi-rigid operators and hyper-recurrence
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910384668016640 |
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| author | Saavedra, Manuel Stadlbauer, Manuel |
| author_facet | Saavedra, Manuel Stadlbauer, Manuel |
| contents | We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach space is quasi-rigid if and only if it is a linear factor of a hyper-recurrent operator, and show that the quasi-rigid operators found in Costakis, Manoussos and Parissis's work, along with many others, are, in fact, hyper-recurrent operators. Furthermore, we provide a negative answer, using a class of operators introduced by Tapia, to the question by Costakis et al. whether $T \oplus T$ is recurrent whenever $T$ is. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-rigid operators and hyper-recurrence Saavedra, Manuel Stadlbauer, Manuel Functional Analysis Dynamical Systems 47A16, 37B20 We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach space is quasi-rigid if and only if it is a linear factor of a hyper-recurrent operator, and show that the quasi-rigid operators found in Costakis, Manoussos and Parissis's work, along with many others, are, in fact, hyper-recurrent operators. Furthermore, we provide a negative answer, using a class of operators introduced by Tapia, to the question by Costakis et al. whether $T \oplus T$ is recurrent whenever $T$ is. |
| title | Quasi-rigid operators and hyper-recurrence |
| topic | Functional Analysis Dynamical Systems 47A16, 37B20 |
| url | https://arxiv.org/abs/2403.17904 |