Inner ideals and facial structure of the quasi-state space of a JB-algebra
type: Item
instance of: scholarly article
title: Inner ideals and facial structure of the quasi-state space of a JB-algebra
zbMATH Open document ID: 0959.46039
author: Matthew Neal
published in: Journal of Functional Analysis
publication date: 2001-05-01T00:00:00Z
review text: The facial structure associated with a JB-algebra \(A\) is studied in this paper. In particular, the author classifies the \(w^*\)-closed faces ontaining zero of the quasi-state space \(Q(A)\) in terms of the algebraic structure of \(A\). This study provides a new approach to the classification of the \(w^*\)-closed faces of the quasi-state space of a \(C^*\)-algebra. But unlike this special cases, due to Akemann and Pedersen, whose proof uses the Gelfand-Naimark representation, dealing with the general case of a JB-algebra requires the introduction of new techniques including the use of a new inequality of Cauchy-Schwarz type for elements of the dual of a JB-algebra.
Mathematics Subject Classification ID: 46H70
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 1484762
zbMATH Keywords: facial structure
zbMATH Keywords: JB-algebra
zbMATH Keywords: \(w^*\)-closed faces
zbMATH Keywords: quasi-state space of a \(C^*\)-algebra
zbMATH Keywords: inequality of Cauchy-Schwarz type
zbMATH Keywords: dual of a JB-algebra
reviewed by: Antonio Fernández López
MaRDI profile type: Publication
full work available at URL: jfan.2000.3577
OpenAlex ID: W2002760026
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DOI: 10.1006/JFAN.2000.3577
description: scientific article; zbMATH DE number 1484762