Completely positive maps of the Cuntz algebras
type: Item
instance of: scholarly article
title: Completely positive maps of the Cuntz algebras
zbMATH Open document ID: 0899.46042
author: Rita Zuccante
published in: Journal of Functional Analysis
publication date: 1998-11-12T00:00:00Z
review text: The author constructs a covariant functor from the category whose objects are separable Hilbert spaces and whose morphisms are contractions, into the category whose objects are unital \(C^*\)-algebras and whose morphisms are completely positive, identity preserving maps. The \(C^*\)-algebras involved are isomorphic to the Cuntz algebra \({\mathcal O}_\infty\) and the functor extends the canonical action of the group of unitaries on the generating Hilbert space. For a related result see \textit{O. Bratteli}, \textit{D. E. Evans}, \textit{F. M. Goodman} and \textit{P. E. T. Jørgensen} [Publ. Res. Inst. Math. Sci. 22, 103-117 (1986; Zbl 0611.46064)].
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 1006667
zbMATH Keywords: covariant functor
zbMATH Keywords: Cuntz algebra
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: jfan.1996.2994
OpenAlex ID: W1986549933
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DOI: 10.1006/JFAN.1996.2994
description: scientific article; zbMATH DE number 1006667