Disjoint hypercyclicity, Sidon sets and weakly mixing operators
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910436873469952 |
|---|---|
| author | Cardeccia, Rodrigo |
| author_facet | Cardeccia, Rodrigo |
| contents | 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 $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16617 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Disjoint hypercyclicity, Sidon sets and weakly mixing operators Cardeccia, Rodrigo Functional Analysis 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 $n$. |
| title | Disjoint hypercyclicity, Sidon sets and weakly mixing operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2203.16617 |