Disjoint hypercyclicity, Sidon sets and weakly mixing operators

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Cardeccia, Rodrigo
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