Frequently hypercyclic bilateral shifts

TL;DR

This paper investigates the conditions under which bilateral weighted shifts on Banach sequence spaces are frequently hypercyclic, providing new insights into the behavior of their inverses and extending the understanding of upper frequent hypercyclicity.

Contribution

It establishes that the inverse of an upper frequently hypercyclic bilateral weighted shift is also upper frequently hypercyclic and characterizes when bilateral shifts are (upper) frequently hypercyclic.

Findings

Inverse of upper frequently hypercyclic bilateral shifts is also upper frequently hypercyclic

Characterization of (upper) frequent hypercyclicity for bilateral weighted shifts

Extension of hypercyclicity results to Banach sequence spaces

Abstract

It is not known if the inverse of a frequently hypercyclic bilateral weighted shift on $c_0(\mathbb{Z})$ is again frequently hypercyclic. We show that the corresponding problem for upper frequent hypercyclicity has a positive answer. We characterise, more generally, when bilateral weighted shifts on Banach sequence spaces are (upper) frequently hypercyclic.