Two remarks on the set of recurrent vectors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866910898480742400 |
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| author | López-Martínez, Antoni Menet, Quentin |
| author_facet | López-Martínez, Antoni Menet, Quentin |
| contents | We solve in the negative two open problems, related to the linear and topological structure of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of this paper. Firstly, we show that there exist recurrent operators whose set of recurrent vectors is not dense lineable; and secondly, we construct operators which are reiteratively recurrent and cyclic, but whose set of reiteratively recurrent vectors is meager. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two remarks on the set of recurrent vectors López-Martínez, Antoni Menet, Quentin Functional Analysis Dynamical Systems 47A16, 37B20, 46B87 We solve in the negative two open problems, related to the linear and topological structure of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of this paper. Firstly, we show that there exist recurrent operators whose set of recurrent vectors is not dense lineable; and secondly, we construct operators which are reiteratively recurrent and cyclic, but whose set of reiteratively recurrent vectors is meager. |
| title | Two remarks on the set of recurrent vectors |
| topic | Functional Analysis Dynamical Systems 47A16, 37B20, 46B87 |
| url | https://arxiv.org/abs/2309.07573 |