Isometries of JB-algebras
type: Item
instance of: scholarly article
title: Isometries of JB-algebras
zbMATH Open document ID: 0834.17048
DOI: 10.1007/BF02567998
published in: Manuscripta Mathematica
publication date: 1995-08-29T00:00:00Z
full work available at URL: https://eudml.org/doc/156058
review text: The main theorem of this paper proves that for a bijective linear map \(F: A\to B\) between JB-algebras the nice equivalence of each of the following assertions is satisfied: i) \(F\) is an isometry; ii) \(F= b\circ G\) where \(G\) is an algebra isomorphism between both JB-algebras and \(b^2= \text{Id}\) with \(b\) belonging to the algebra of multipliers of \(B\); iii) \(F(x^3)= F(x)^3\) for all \(x\) in \(A\); iv) \(F( \{xyz\})= \{F(x) F(y) F(z)\}\) for any \(x, y,z\in A\). In the particular case of JBW-factors the bijective linear isometries are of the form \(\varepsilon G\) for \(\varepsilon= \pm1\) and \(G\) an algebra isomorphism. Section 2 is then devoted to the determination of the algebra isomorphisms between JBW- factors of type I different from \(H_3 (\mathbb{O})\).
reviewed by: José Antonio Cuenca Mira
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46H70
zbMATH DE Number: 784033
zbMATH Keywords: JBW-algebra
zbMATH Keywords: JB-algebras
zbMATH Keywords: linear isometries
zbMATH Keywords: JBW-factors
author: José M. Isidro
author: Ángel Rodríguez Palacios
MaRDI profile type: Publication
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OpenAlex ID: W1995353412
description: scientific article; zbMATH DE number 784033