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.

arXiv comment12 pages, 2 figures