Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
type: Item
instance of: scholarly article
title: Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
zbMATH Open document ID: 0912.46070
author: Paul S. Muhly
author: Baruch Solel
published in: Journal of Functional Analysis
publication date: 1999-05-26T00:00:00Z
review text: The tensor algebra associated to a \(C^*\)-correspondence (or Hilbert \(C^*\)-module) is a non-commutative generalization of the disk algebra. The main result of this work is that for certain \(C^*\)-correspondences the \(C^*\)-envelope of the tensor algebra is the Cuntz-Pimsner algebra of the correspondence. Along the way results on the existence and structure of dilations, coisometric extensions and commutant lifting are obtained.
Mathematics Subject Classification ID: 46L89
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 1215586
zbMATH Keywords: tensor algebra associated to a \(C^*\)-correspondence
zbMATH Keywords: Hilbert \(C^*\)-module
zbMATH Keywords: non-commutative generalization of the disk algebra
zbMATH Keywords: \(C^*\)-envelope
zbMATH Keywords: Cuntz-Pimsner algebra
zbMATH Keywords: structure of dilations
zbMATH Keywords: coisometric extensions
zbMATH Keywords: commutant lifting
reviewed by: G. Loupias
MaRDI profile type: Publication
full work available at URL: jfan.1998.3294
OpenAlex ID: W1977621603
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DOI: 10.1006/JFAN.1998.3294
description: scientific article; zbMATH DE number 1215586