A hypercyclicity criterion for non-metrizable topological vector spaces
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913256393670656 |
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| author | Peris, Alfred |
| author_facet | Peris, Alfred |
| contents | We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Domański \cite{bd12}, and the "snake shift" constructed in \cite{bfpw} on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space $Y$ for which the operator restricted to $Y$ is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1804_04884 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A hypercyclicity criterion for non-metrizable topological vector spaces Peris, Alfred Functional Analysis Dynamical Systems 47A16 We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Domański \cite{bd12}, and the "snake shift" constructed in \cite{bfpw} on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space $Y$ for which the operator restricted to $Y$ is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces. |
| title | A hypercyclicity criterion for non-metrizable topological vector spaces |
| topic | Functional Analysis Dynamical Systems 47A16 |
| url | https://arxiv.org/abs/1804.04884 |