Dynamics of weighted shifts on $\ell^p$-sums and $c_0$-sums
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909292191285248 |
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| author | Menet, Quentin Papathanasiou, Dimitris |
| author_facet | Menet, Quentin Papathanasiou, Dimitris |
| contents | We investigate a generalization of weighted shifts where each weight $w_k$ is replaced by an operator $T_k$ going from a Banach space $X_k$ to another one $X_{k-1}$. We then look if the obtained shift operator $B_{(T_k)}$ defined on the $\ell^p$-sum (or the $c_0$-sum) of the spaces $X_k$ is hypercyclic, weakly mixing, mixing, chaotic or frequently hypercyclic. We also compare the dynamical properties of $T$ and of the corresponding shift operator $B_T$. Finally, we interpret some classical criteria in Linear Dynamics in terms of the dynamical properties of a shift operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_11153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of weighted shifts on $\ell^p$-sums and $c_0$-sums Menet, Quentin Papathanasiou, Dimitris Functional Analysis 47A16 We investigate a generalization of weighted shifts where each weight $w_k$ is replaced by an operator $T_k$ going from a Banach space $X_k$ to another one $X_{k-1}$. We then look if the obtained shift operator $B_{(T_k)}$ defined on the $\ell^p$-sum (or the $c_0$-sum) of the spaces $X_k$ is hypercyclic, weakly mixing, mixing, chaotic or frequently hypercyclic. We also compare the dynamical properties of $T$ and of the corresponding shift operator $B_T$. Finally, we interpret some classical criteria in Linear Dynamics in terms of the dynamical properties of a shift operator. |
| title | Dynamics of weighted shifts on $\ell^p$-sums and $c_0$-sums |
| topic | Functional Analysis 47A16 |
| url | https://arxiv.org/abs/2408.11153 |