Conjugate dynamical systems on \(C^*\)-algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.46059
author: Kenneth R. Davidson
author: Evgenios T. A. Kakariadis
publication date: 2014-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.3016
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L99
zbMATH DE Number: 6340352
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: \(C^*\)-dynamical systems
zbMATH Keywords: semicrossed products
zbMATH Keywords: isometrical isomorphism
MaRDI profile type: Publication
OpenAlex ID: W2593841525
arXiv ID: 1205.3016
DOI: 10.1093/IMRN/RNS253
published in: IMRN. International Mathematics Research Notices
title: Conjugate dynamical systems on \(C^*\)-algebras
review text: The main results of the paper are as follows. If \((A,\alpha)\) and \((B,\beta)\) are unital \(C^*\)-algebra dynamical systems, where \(\alpha\) is either injective or surjective, then \(A \times_{\alpha} \mathbb{Z}_{+}\) and \(B \times_{\beta} \mathbb{Z}_{+}\) are isometrically isomorphic \(\Longleftrightarrow (A,\alpha), (B,\beta)\) are outer conjugate. Let \((A,\alpha), (B,\beta)\) be unital \(C^*\)-algebra dynamical systems. If one of some properties such as \(A\) has trivial center, \(A\) is abelian, \(A\) is finite or \(\alpha (A)'\) is finite, \(\alpha(R_{\alpha})=R_{\alpha}\), and \(\alpha(\operatorname{ann}(R_{\alpha})) \subseteq \operatorname{ann}(R_{\alpha})\) holds, then \(A \times_{\alpha} \mathbb{Z}_{+}\) and \(B \times_{\beta} \mathbb{Z}_{+}\) are isometrically isomorphic if and only if \((A,\alpha)\) and \((B,\beta)\) are outer conjugate.
reviewed by: Victor Sharapov
description: scientific article; zbMATH DE number 6340352