Jordan structures in Banach spaces
type: Item
instance of: scholarly article
title: Jordan structures in Banach spaces
zbMATH Open document ID: 1287.46053
author: Cho-Ho Chu
published in: Operators and Matrices
publication date: 2012-09-14T00:00:00Z
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 6082492
zbMATH Keywords: Jordan triple system
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: \(JB^*\)-triple
MaRDI profile type: Publication
full work available at URL: oam-06-25
OpenAlex ID: W2330022946
DOI: 10.7153/OAM-06-25
review text: The author revisits the proof of the following result by \textit{W. Kaup} [Math. Appl., Dordr. 303, 204--214 (1994; Zbl 0810.46075)]: A bounded symmetric domain in a complex Banach space is biholomorphically equivalent to the open unit ball of a \(JB^*\)-triple. A \(JB^*\)-triple is a complex Banach space with a Jordan triple product and an involution satisfying some conditions. Further, the author gives some applications of \(JB^*\)-triples. One of them is as follows: A linear bijection \(\varphi \) between \(JB^*\)-triples is an isometry if and only if \(\varphi \) is a triple homomorphism, that is, \(\varphi \) preserves the triple product NEWLINE\[NEWLINE\varphi (\{a,b,c\})=\{\varphi (a),\varphi (b),\varphi (c)\}.NEWLINE\]
reviewed by: Jacques Faraut
description: scientific article; zbMATH DE number 6082492