On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914543560556544 |
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| author | Albuquerque, Nacib G. Alves, Thiago R. Botelho, Geraldo Fávaro, Vinícius V. |
| author_facet | Albuquerque, Nacib G. Alves, Thiago R. Botelho, Geraldo Fávaro, Vinícius V. |
| contents | Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof technique we develop also allows us to prove that $B$ admits a hypercyclic subspace free of $\mathscr{U}$-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common $\mathscr{U}$-frequently hypercyclic subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07563 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces Albuquerque, Nacib G. Alves, Thiago R. Botelho, Geraldo Fávaro, Vinícius V. Functional Analysis Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof technique we develop also allows us to prove that $B$ admits a hypercyclic subspace free of $\mathscr{U}$-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common $\mathscr{U}$-frequently hypercyclic subspaces. |
| title | On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2605.07563 |