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 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 50 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.15672/hujms.791344
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, zbMATH
  • Page Numbers: pp.1609-1619

Abstract

We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on c0(\N)" role="presentation">c0(\N) and ℓp(\N)" role="presentation">p(\N), p∈[1,∞)" role="presentation">p[1,), 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 c0(\N)" role="presentation">c0(\N) and ℓp(\N)" role="presentation">p(\N), p∈[1,∞)" role="presentation">p[1,).