Strong transitivity properties for operators
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Acceso en línea: | |
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| _version_ | 1866914705716543488 |
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| author | Bès, Juan Menet, Quentin Peris, Alfredo de Dios, Yunied Puig |
| author_facet | Bès, Juan Menet, Quentin Peris, Alfredo de Dios, Yunied Puig |
| contents | Given a Furstenberg family $\mathscr{F}$ of subsets of $\mathbb{N}$, an operator $T$ on a topological vector space $X$ is called $\mathscr{F}$-transitive provided for each non-empty open subsets $U$, $V$ of $X$ the set $\{n\in \mathbb{Z}_+ : T^n(U)\cap V\neq\emptyset\}$ belongs to $\mathscr{F}$. We classify the topologically transitive operators with a hierarchy of $\mathscr{F}$-transitive subclasses by considering families $\mathscr{F}$ that are determined by various notions of largeness and density in $\mathbb{Z}_+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_03724 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Strong transitivity properties for operators Bès, Juan Menet, Quentin Peris, Alfredo de Dios, Yunied Puig Functional Analysis 47A16 Given a Furstenberg family $\mathscr{F}$ of subsets of $\mathbb{N}$, an operator $T$ on a topological vector space $X$ is called $\mathscr{F}$-transitive provided for each non-empty open subsets $U$, $V$ of $X$ the set $\{n\in \mathbb{Z}_+ : T^n(U)\cap V\neq\emptyset\}$ belongs to $\mathscr{F}$. We classify the topologically transitive operators with a hierarchy of $\mathscr{F}$-transitive subclasses by considering families $\mathscr{F}$ that are determined by various notions of largeness and density in $\mathbb{Z}_+$. |
| title | Strong transitivity properties for operators |
| topic | Functional Analysis 47A16 |
| url | https://arxiv.org/abs/1703.03724 |