New classes of hypercyclic Toeplitz operators

TL;DR

This paper investigates the hypercyclicity of a new class of Toeplitz operators on the Hardy space, linking it to cyclicity of functions and providing novel sufficient conditions for hypercyclicity.

Contribution

It introduces new classes of hypercyclic Toeplitz operators with symbols combining rational functions and bounded analytic functions, expanding understanding of hypercyclicity criteria.

Findings

Established connections between hypercyclicity and cyclicity of function families.

Derived new sufficient conditions for hypercyclicity using results by B. Solomyak.

Identified classes of Toeplitz operators exhibiting hypercyclic behavior.

Abstract

We study hypercyclicity of Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $R(\overline{z}) +\phi(z)$, where $R$ is a rational function and $\phi \in H^\infty(\mathbb{D})$. We relate this problem to cyclicity of certain families of functions for analytic Toeplitz operators and give new sufficient conditions for hypercyclicity based on deep results of B. Solomyak.