Disjoint hypercyclicity, Sidon sets and weakly mixing operators
| Autor: | Cardeccia, Rodrigo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Ergod. Th. Dynam. Sys. 44 (2024) 1315-1329 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/etds.2023.54 |
| Popis: | We prove that a finite set of natural numbers $J$ satisfies that $J\cup\{0\}$ is not Sidon if and only if for any operator $T$, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that $T$ is weakly mixing. As an application we show the existence of a non weakly mixing operator $T$ such that $T\oplus T^2\ldots \oplus T^n$ is hypercyclic for every $n$. |
| Databáze: | arXiv |
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