Biweights and \(^{\ast}\)-homomorphisms of partial \(^{\ast}\)-algebras
type: Item
instance of: scholarly article
title: Biweights and \(^{\ast}\)-homomorphisms of partial \(^{\ast}\)-algebras
zbMATH Open document ID: 1160.47057
DOI: 10.1155/IJMMS/2006/54793
author: J. P. Antoine
author: Camillo Trapani
author: F. Tschinke
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-07-28T00:00:00Z
full work available at URL: https://eudml.org/doc/55331
review text: Biweights on partial \(*\)-algebras allow a GNS construction and thus permit to develop from there a representation theory for partial \(*\)-algebras. Nevertheless, biweights exhibit unfamiliar features: the restriction of a biweight on a partial \(*\)-subalgebra is not necessarily a biweight. The authors present sufficient conditions under which \(\varphi\circ\Phi\) is a biweight on \({\mathfrak A}_1\), where \(\Phi\) is a \(*\)-homomorphism from a partial \(*\)-algebra \({\mathfrak A}_1\) to a partial \(*\)-algebra \({\mathfrak A}_2\) and \(\varphi\) is a biweight on \({\mathfrak A}_2\). Furthermore, they investigate the continuity of a \(*\)-homomorphism from a normed partial \(*\)-algebra to another one, making use of unbounded \(C^*\)-seminorms defined by biweights.
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 46K05
zbMATH DE Number: 5304381
reviewed by: A. Inoue
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5304381