Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras
type: Item
instance of: scholarly article
title: Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras
zbMATH Open document ID: 0749.47030
author: Camillo Trapani
author: J. P. Antoine
author: A. Inoue
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1992-09-26T00:00:00Z
review text: This is the second paper on partial \(Op^*\)-algebras by the authors, which is devoted to the study of the theory of representations. However, the definitions for partial \(Op^*\)-algebras seem to be too general to obtain any interesting results. Therefore the authors introduce and study a subclass, called partial \(GW^*\)-algebras. The Gel'fand-Naimark-Segal (GNS) construction id given for partial \(GW^*\)-algebras. Also, for the abelian partial \(GW^*\)-algebras, they extend Power's results about the standardness of \(GNS\) representations of abelian partial \(*\)- algebras. [For part I see ibid. 26, No. 2, 359-395 (1990; Zbl 0724.47020).].
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 46H15
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 55942
zbMATH Keywords: Gel'fand-Naimark-Segal construction
zbMATH Keywords: partial \(Op^*\)-algebras
zbMATH Keywords: representations
zbMATH Keywords: partial \(GW^*\)-algebras
zbMATH Keywords: \(GNS\) representations
reviewed by: Wong, Pak-ken
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195169662
OpenAlex ID: W1999240682
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DOI: 10.2977/PRIMS/1195169662
description: scientific article; zbMATH DE number 55942