Weakly mixing operators on topological vector spaces
type: Item
instance of: scholarly article
title: Weakly mixing operators on topological vector spaces
zbMATH Open document ID: 1238.47006
DOI: 10.5052/RACSAM.2010.25
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2011-07-18T00:00:00Z
review text: Let \(X\) be a topological space and let \(T\) be a continuous map from \(X\) into itself. The dynamical system \((X,T)\) is called weakly mixing if, for any four nonempty open sets \(U_1,\, U_2,\, V_1,\;V_2\subset X\), there exists some \(n\in\mathbb{N}\) such that \(T^n(U_1)\cap V_1\not=\emptyset\) and \(T^n(U_2)\cap V_2\not=\emptyset\). In the paper under review, the authors review known characterizations of weakly dynamical systems. In the second part of the paper, the authors obtain additional characterizations of, and sufficient conditions for, the (weak) mixing property in the case of linear dynamical systems, that is, dynamical systems \(T: X\to X\) given by continuous linear operators on a topological vector space \(X\). They end the paper collecting some open problems on the weak mixing property.
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 5925099
zbMATH Keywords: weakly mixing maps
zbMATH Keywords: mixing maps
zbMATH Keywords: weakly mixing operators
zbMATH Keywords: hypercyclic operators
author: Karl-Goswin Grosse-Erdmann
author: A. Peris
MaRDI profile type: Publication
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full work available at URL: racsam.2010.25
OpenAlex ID: W1500097775
description: scientific article; zbMATH DE number 5925099