Frequently recurrent backward shifts
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913054048911360 |
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| author | Cardeccia, Rodrigo Muro, Santiago |
| author_facet | Cardeccia, Rodrigo Muro, Santiago |
| contents | We study frequently recurrent unilateral and bilateral backward shift operators on Fréchet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so that the operator is frequently recurrent. As a consequence, we provide two different characterizations for frequently recurrent backward shift operators and we show dense lineability of the set of the set of frequently recurrent vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frequently recurrent backward shifts Cardeccia, Rodrigo Muro, Santiago Functional Analysis Dynamical Systems 47A16, 47B37, 37B20, 37A46, 47A35 We study frequently recurrent unilateral and bilateral backward shift operators on Fréchet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so that the operator is frequently recurrent. As a consequence, we provide two different characterizations for frequently recurrent backward shift operators and we show dense lineability of the set of the set of frequently recurrent vectors. |
| title | Frequently recurrent backward shifts |
| topic | Functional Analysis Dynamical Systems 47A16, 47B37, 37B20, 37A46, 47A35 |
| url | https://arxiv.org/abs/2407.11799 |