On strictly weakly mixing \(C^*\)-dynamical systems
type: Item
instance of: scholarly article
title: On strictly weakly mixing \(C^*\)-dynamical systems
zbMATH Open document ID: 1171.37006
publication date: 2008-09-02T00:00:00Z
review text: The question of how strict ergodicity is related to mixing conditions is studied in a noncommutative setting. One considers strictly ergodic and strictly weakly mixing \(C^{\ast }\)- dynamical systems. Different notions of mixing (weak, strictly weak, complete mixing, etc.) and strictly ergodic state-preserving \(C^{\ast }\)- dynamical systems are defined and their properties are considered. It is established that a system is strictly weakly mixing if and only if its tensor product is strictly ergodic and strictly weakly mixing. Some weighted uniform ergodic theorems with respect to S-Besicovitch sequences for strictly weakly mixing dynamical systems are also investigated. Illustrative examples of strictly weakly mixing dynamical systems are given.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 37A55
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 5319691
zbMATH Keywords: strict ergodicity
zbMATH Keywords: strictly weak mixing
zbMATH Keywords: \(C^*\)-dynamical system
zbMATH Keywords: S-Besicovitch sequence
author: Farruh Mukhamedov
MaRDI profile type: Publication
full work available at URL: s10688-007-0030-y
OpenAlex ID: W2020641580
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DOI: 10.1007/S10688-007-0030-Y
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 5319691