Hypercyclicity of Toeplitz operators with smooth symbols

2025/02/05 by Fricain, Emmanuel, Grivaux, Sophie, Ostermann, Maëva · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.03303

Abstract

This paper is devoted to the study of the dynamics of Toeplitz operators T_F with smooth symbols F on the Hardy spaces of the unit disk H^p, p>1. Building on a model theory for Toeplitz operators on H² developed by Yakubovich in the 90's, we carry out an in-depth study of hypercyclicity properties of such operators. Under some rather general smoothness assumptions on the symbol, we provide some necessary/sufficient/necessary and sufficient conditions for T_F to be hypercyclic on H^p. In particular, we extend previous results on the subject by Baranov-Lishanskii and Abakumov-Baranov-Charpentier-Lishanskii. We also study some other dynamical properties for this class of operators.

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• Introduction To The Dynamical Properties Of Toeplitz Operators On The Hardy Space Of The Unit Disc

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