Dynamics of composition operators on weighted Bergman spaces
type: Item
instance of: scholarly article
title: Dynamics of composition operators on weighted Bergman spaces
zbMATH Open document ID: 1357.47012
author: Liang Zhang
author: Ze-Hua Zhou
published in: Indagationes Mathematicae. New Series
publication date: 2016-01-12T00:00:00Z
review text: The aim of the paper under review is to study multiples of composition operators associated to linear fractional maps on weighted Bergman spaces, from the point of view of linear dynamics. Let \(\alpha >-1\), \(1<p<+\infty \), and \(\varphi \) a linear fractional map on the unit disk \(\mathbb{D}\). The composition operator \(C_{\varphi }:f\longmapsto f\circ \varphi \) is always bounded on the Bergman space \(A_{\alpha }^{p}\). The author characterizes the frequent hypercyclicity of multiples \(\lambda C_{\varphi }\) of \(C_{\varphi }\), when \(\varphi\) is either a parabolic automorphism, a hyperbolic automorphism, or a hyperbolic non-automorphism of \(\mathbb{D}\). In all these cases, \(\lambda C_{\varphi }\) is frequently hypercyclic on \(A_{\alpha }^{p}\) if and only if it is hypercyclic, if and only if it is mixing. The proofs rely on classical criteria, such as the Frequent Hypercyclicity Criterion. Disjoint hypercyclicity of finite tuples of composition operators on \(A_{\alpha }^{p}\) associated to linear fractional maps is also studied.
reviewed by: Sophie Grivaux
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 6529317
zbMATH Keywords: frequently hypercyclic
zbMATH Keywords: disjoint hypercyclic
zbMATH Keywords: composition operators
zbMATH Keywords: weighted Bergman spaces
MaRDI profile type: Publication
full work available at URL: j.indag.2015.11.012
OpenAlex ID: W2188540565
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DOI: 10.1016/J.INDAG.2015.11.012
description: scientific article; zbMATH DE number 6529317