Approximation of chaotic operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 1261.47016
author: Bingzhe Hou
author: Geng Tian
author: Sen Zhu
publication date: 2012-06-13T00:00:00Z
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 6045977
zbMATH Keywords: Li-Yorke chaotic operator
zbMATH Keywords: distributionally chaotic operator
zbMATH Keywords: hypercyclic operator
zbMATH Keywords: connectedness
MaRDI profile type: Publication
title: Approximation of chaotic operators
published in: Journal of Operator Theory
review text: In the present paper, Li-Yorke and distributionally chaotic linear operators on Hilbert spaces are studied. The closures and the interiors of the set of all Li-Yorke chaotic operators or all distributionally chaotic operators are discussed. The arcwise connectedness of these sets is proved. The authors also obtain the following relation between hypercyclic operators and distributionally chaotic operators: the set of all hypercyclic operators belongs to the closure of the set of all distributionally chaotic operators. The relation between norm-unimodal operators and distributionally chaotic operators is also obtained.
reviewed by: Michael Perelmuter
description: scientific article; zbMATH DE number 6045977