New classes of hypercyclic Toeplitz operators

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.Comment: 12 pages, 2 figure

NEW CLASSES OF HYPERCYCLIC TOEPLITZ OPERATORS

International audienceWe study hypercyclicity of Toeplitz operators in the Hardy space H 2 (D) with symbols of the form R(z) + ϕ(z), where R is a rational function and ϕ ∈ H ∞ (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