Separate weak\(^*\)-continuity of the triple product in dual real JB\(^*\)-triples
type: Item
instance of: scholarly article
title: Separate weak\(^*\)-continuity of the triple product in dual real JB\(^*\)-triples
zbMATH Open document ID: 0977.17032
author: R. Smith
published in: Mathematische Zeitschrift
publication date: 2000-10-26T00:00:00Z
review text: \textit{J. M. Isodro, W. Kaup} and \textit{A. Rodríguez Palacio} [Manuscr. Math. 86, 311-335 (1995; Zbl 0834.17047)] introduced a concept of real JB*-triple as a real form of a complex JB*-triple. The class of real JB*-triples include all JB-algebras, all real \(C^*\)-algebras, all J*B-algebras and obviously all complex JB*-triples. In this paper we prove that, if \(E\) is a real JB*-triple having a predual \(E_*\), then \(E_*\) is the unique predual of \(E\) and the triple product on \(E\) is separately \(\sigma(E,E_*)\)-continuous, extending the important result due to \textit{T. Barton} and \textit{R. M. Timoney} for complex JB*-triples [Math. Scand. 59, 177-191 (1986; Zbl 0621.46044)].
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 1515375
zbMATH Keywords: JB*-algebras
zbMATH Keywords: complex Banach space
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: weak*-continuity
MaRDI profile type: Publication
DOI: 10.1007/S002090000094
description: scientific article; zbMATH DE number 1515375