Disjoint and simultaneous hypercyclic Rolewicz-type operators

Year 2021, Volume: 50 Issue: 6, 1609 - 1619, 14.12.2021

Nurhan Çolakoğlu , Özgür Martin

https://doi.org/10.15672/hujms.791344

Cited By: 1

Abstract

We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$, which are a generalization of the unilateral backward shift operator. We show that disjoint hypercyclicity and disjoint supercyclicity are equivalent among a subfamily of these operators and disjoint hypercyclic unilateral Rolewicz-type operators always satisfy the Disjoint Hypercyclicity Criterion. We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$.

Keywords

hypercyclic vectors, hypercyclic operators, disjoint hypercyclicity, simultaneous hypercyclicity

Supporting Institution

Mimar Sinan Fine Arts University Scientific Research Project

Project Number

2016-18

Thanks

The first author was partially supported by Istanbul Technical University Scientific Research Project [grant no. TAB-2017-40552]. The second author was partially supported by Mimar Sinan Fine Arts University Scientific Research Project [grant no. 2016-18].

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