A continuous-parameter Katznelson-Tzafriri theorem for algebras of analytic functions

Abstract

We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators which have functional calculi with respect to some larger algebras.

arXiv commentNew title, to reflect the improvement in our main result. Accepted for publication in Studia Mathematica