Frequently recurrent operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916149240791040 |
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| author | Bonilla, Antonio Grosse-Erdmann, Karl-G. López-Martínez, Antoni Peris, Alfred |
| author_facet | Bonilla, Antonio Grosse-Erdmann, Karl-G. López-Martínez, Antoni Peris, Alfred |
| contents | Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the corresponding notion of hypercyclicity, the influence of power boundedness, and the interplay between recurrence and spectral properties. We obtain, in particular, Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-recurrence under very weak assumptions on the Furstenberg family $\mathcal{F}$. This allows us, as a by-product, to deduce Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-hypercyclicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_11428 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Frequently recurrent operators Bonilla, Antonio Grosse-Erdmann, Karl-G. López-Martínez, Antoni Peris, Alfred Functional Analysis Dynamical Systems 47A16 (Primary) 47B37 (Secondary) Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the corresponding notion of hypercyclicity, the influence of power boundedness, and the interplay between recurrence and spectral properties. We obtain, in particular, Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-recurrence under very weak assumptions on the Furstenberg family $\mathcal{F}$. This allows us, as a by-product, to deduce Ansari- and Léon-Müller-type theorems for $\mathcal{F}$-hypercyclicity. |
| title | Frequently recurrent operators |
| topic | Functional Analysis Dynamical Systems 47A16 (Primary) 47B37 (Secondary) |
| url | https://arxiv.org/abs/2006.11428 |