Disjoint and simultaneous hypercyclic Rolewicz-type operators

---

Çolakoğlu N. , Martin Ö.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.6, pp.1609-1619, 2021 (Journal Indexed in SCI Expanded)

• Publication Type: Article / Article
• Volume: 50 Issue: 6
• Publication Date: 2021
• Doi Number: 10.15672/hujms.791344
• Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Page Numbers: pp.1609-1619

Abstract

We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0\left(\text{N}\right)$ and ${\ell }^p\left(\text{N}\right)$, $p\in [1,\infty )$, 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 $c_0\left(\text{N}\right)$ and ${\ell }^p\left(\text{N}\right)$, $p\in [1,\infty )$.