New classes of hypercyclic Toeplitz operators

Abstract

We study hypercyclicity of Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $R(\overline{z})+\varphi (z)$, where $R$ is a rational function and $\varphi \in H^{\infty }(\mathbb{D})$. 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.

12 pages, 2 figures