Jordan triple maps.
type: Item
instance of: scholarly article
title: Jordan triple maps.
zbMATH Open document ID: 1061.47033
author: Fangyan Lu
published in: Linear Algebra and its Applications
publication date: 2003-12-04T00:00:00Z
review text: Let \(r\) be a nonzero rational number. A map \(\phi : A \to B\) between Banach algebras \(A\) and \(B\) is said to be a \(r\)-Jordan triple map if \(\phi(r(abc+cba)) = r(\phi(a)\phi(b)\phi(c)+\phi(c)\phi(b)\phi(a))\) for all \(a,b,c \in A\). Suppose that \(A\) is a standard operator algebra. The author proves, among other things, that a bijective \(r\)-Jordan triple map is necessarily additive.
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 2013062
zbMATH Keywords: triple maps
zbMATH Keywords: standard operator algebras
zbMATH Keywords: additivity
reviewed by: Cătălin Badea
MaRDI profile type: Publication
full work available at URL: j.laa.2003.06.004
OpenAlex ID: W2061617430
cites work: Jordan mappings of semiprime rings
cites work: Multiplicative mappings of operator algebras
cites work: Additivity of Jordan maps on standard operator algebras
cites work: Jordan Maps on Associative Algebras
cites work: When are Multiplicative Mappings Additive?
cites work: On isomorphisms of standard operator algebras
cites work: Q4530604
cites work: Automorphisms of the poset of skew projections
DOI: 10.1016/J.LAA.2003.06.004
description: scientific article; zbMATH DE number 2013062