Real normed Jordan Banach algebras with an involution
type: Item
instance of: scholarly article
title: Real normed Jordan Banach algebras with an involution
zbMATH Open document ID: 0581.46059
DOI: 10.1007/BF01193684
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The subject of the paper are the Jordan analogues of real \(C^*\)- algebras. A \(J^*B\)-algebra is a real Jordan algebra with unit and an involution * with a complete algebra norm such that \(\| U_ xx^*\| =\| x\|^ 3\) and \(\| x^*x\| \leq \| x^*x+y^*y\|.\) In the first part of the paper the complexification theorem is proved: the complexification of a \(J^*B\)-algebra is a \(JB^*\)-algebra. The second part treats the classification of the finite dimensional \(J^*B\)-algebras.
Mathematics Subject Classification ID: 46L99
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46K99
zbMATH DE Number: 3929735
zbMATH Keywords: Jordan analogues of real \(C^*\)-algebras
zbMATH Keywords: \(J^*B\)-algebra
zbMATH Keywords: Jordan algebra
zbMATH Keywords: involution
zbMATH Keywords: complexification
zbMATH Keywords: classification of the finite dimensional \(J^*B\)-algebras
author: Klaus Alvermann
MaRDI profile type: Publication
cites work: Q3215824
cites work: Q5186181
cites work: Q5622399
cites work: Jordan \(C^*\)-algebras
cites work: A Vidav theorem for Banach Jordan algebras
description: scientific article; zbMATH DE number 3929735