Inverse of frequently hypercyclic operators

TL;DR

This paper constructs an example of an invertible operator on ll^1(N) that is frequently hypercyclic, but its inverse does not share this property, highlighting a nuanced behavior in operator dynamics.

Contribution

It demonstrates that the inverse of a frequently hypercyclic operator need not be frequently hypercyclic, providing a counterexample in the context of ll^1 spaces.

Findings

Existence of invertible frequently hypercyclic operators on ll^1(N)

Inverse of such operators may not be frequently hypercyclic

Counterexample challenges assumptions about inverse properties in hypercyclic operators

Abstract

We show that there exists an invertible frequently hypercyclic operator on $\ell^1(\mathbb{N})$ whose inverse is not frequently hypercyclic.