Dynamics of shift operators on non-metrizable sequence spaces
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866914705763729408 |
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| author | Bonet, José Kalmes, Thomas Peris, Alfred |
| author_facet | Bonet, José Kalmes, Thomas Peris, Alfred |
| contents | We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical properties for weighted generalized backward shifts on Köthe coechelon sequence spaces $k_p((v^{(m)})_{m\in\mathbb{N}})$ in terms of the defining sequence of weights $(v^{(m)})_{m\in\mathbb{N}}$. We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on $\mathscr{S}'(\mathbb{R})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_07513 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Dynamics of shift operators on non-metrizable sequence spaces Bonet, José Kalmes, Thomas Peris, Alfred Functional Analysis 47A16, 47B37 We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical properties for weighted generalized backward shifts on Köthe coechelon sequence spaces $k_p((v^{(m)})_{m\in\mathbb{N}})$ in terms of the defining sequence of weights $(v^{(m)})_{m\in\mathbb{N}}$. We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on $\mathscr{S}'(\mathbb{R})$. |
| title | Dynamics of shift operators on non-metrizable sequence spaces |
| topic | Functional Analysis 47A16, 47B37 |
| url | https://arxiv.org/abs/1911.07513 |