Cyclic composition operators on separable locally compact metric spaces
type: Item
instance of: scholarly article
title: Cyclic composition operators on separable locally compact metric spaces
zbMATH Open document ID: 1462.47021
author: Mohammad Javaheri
published in: Topology and its Applications
publication date: 2019-04-24T00:00:00Z
review text: It is proved that, if a homeomorphism of a separable locally compact metric space has a unique fixed point that is attracting or repelling, then its corresponding composition operator is cyclic. On the real line, it is shown that a composition operator is cyclic if and only if its symbol has at most one fixed point. Other results on the real line and the circle are discussed. This study is motivated by results of \textit{Z. Yin} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 6, Article ID 1750084, 12 p. (2017; Zbl 1370.37074)] who implicitly asked if the no-fixed-point condition is necessary for a composition operator to be cyclic on the real line.
reviewed by: José Bonet
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7047512
zbMATH Keywords: composition operator
zbMATH Keywords: cyclic operator
zbMATH Keywords: function space
MaRDI profile type: Publication
full work available at URL: j.topol.2019.03.001
OpenAlex ID: W2922488300
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Wikidata QID: Q128265915
DOI: 10.1016/J.TOPOL.2019.03.001
description: scientific article; zbMATH DE number 7047512