Point spectrum and hypercyclicity problem for a class of truncated Toeplitz operators

Abstract

In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and antianalytic parts. We show that, for a class of model spaces, truncated Toeplitz operators with symbols of the form Φ(z) = az +b+cz, |a| = |c|, are not hypercyclic.