Dynamics of weighted composition operators
type: Item
instance of: scholarly article
title: Dynamics of weighted composition operators
zbMATH Open document ID: 1325.47018
author: J. Bès
published in: Complex Analysis and Operator Theory
publication date: 2014-08-29T00:00:00Z
review text: In the paper under review, the author is concerned with the dynamics of the weighted composition operator \(C_{\omega,\varphi}: H(\Omega)\to H(\Omega)\) given by \(C_{\omega,\varphi}(f)(z)=\omega(z)(f\circ \varphi)(z)\), for \(z\in \Omega\), where \(H(\Omega)\) denotes the space of holomorphic functions on a simply connected domain \(\Omega\) of the complex field, endowed with the compact open topology, \(\varphi\) is a holomorphic self map of \(\Omega\), and \(\omega\in H(\Omega)\). In particular, the author shows that any such operator \(C_{\omega,\varphi}\) is weakly supercyclic if and only if it is topologically mixing and, in the case that the weight is bounded, if and only if the operator has a hypercyclic subspace. The author also provides conditions on the symbol in order that the operator \(C_{\omega,\varphi}\) is Devaney-chaotic and has a frequently hypercyclic subspace.
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 30K20
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 6336124
zbMATH Keywords: composition operators
zbMATH Keywords: chaotic operators
zbMATH Keywords: hypercyclic operators
zbMATH Keywords: supercyclic operators
MaRDI profile type: Publication
full work available at URL: s11785-012-0281-3
OpenAlex ID: W2068036881
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DOI: 10.1007/S11785-012-0281-3
description: scientific article; zbMATH DE number 6336124