Disjoint and simultaneous hypercyclic Rolewicz-type operators

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

Nurhan ÇOLAKOĞLU Özgür MARTİN

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

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

Abstract

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