Disjoint and Simultaneously Hypercyclic Pseudo-Shifts

TL;DR

This paper characterizes disjoint and simultaneous hypercyclicity for unilateral pseudo-shift operators and weighted shifts on ℓ^p, providing new criteria and extending previous results in operator dynamics.

Contribution

It offers a complete characterization of disjoint and simultaneous hypercyclic tuples of pseudo-shifts and weighted shifts, including criteria satisfaction conditions.

Findings

Characterization of disjoint hypercyclic tuples of pseudo-shifts.

Characterization of simultaneously hypercyclic tuples of weighted shifts.

Tuples of weighted shifts are simultaneously hypercyclic iff they satisfy the Simultaneous Hypercyclicity Criterion.

Abstract

We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on $\ell^p(\mathbb{N})$. As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.