Operator space structure of \(JC^*\)-triples and TROs. I
type: Item
instance of: scholarly article
title: Operator space structure of \(JC^*\)-triples and TROs. I
zbMATH Open document ID: 1251.47063
author: Leslie J. Bunce
author: Brian Feely
author: Richard M. Timoney
published in: Mathematische Zeitschrift
publication date: 2012-05-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.1085
review text: Various universal objects are introduced and studied, among them, the universal TRO (ternary ring of operators) of a \(JC^*\)-triple. These objects are used to study the operator space structure of a \(JC^*\)-triple. The reversible \(JC^*\)-triples are defined and used to obtain a characterization of the universal TROs of a wide class of \(JC^*\)-triples. Then the Cartan factors that are \(JC^*\)-triples are considered. A concrete description of the universal TROs of these Cartan factors is obtained and a result characterizing which of them are universally reversible is proved. In the last section, it is shown that the operator space structures of a \(JC^*\)-triple arising from its concrete realizations as a \(JC^*\)-subtriple of \(B(H)\) are completely determined by certain ideals (operator space ideals) of its universal TRO. This result is applied to give a full description of the operator space structures of the non Hilbertian Cartan factors that are \(JC^*\)-triples, arising from their concrete realizations as \(JC^*\)-subtriples of \(B(H)\).
Mathematics Subject Classification ID: 47L25
Mathematics Subject Classification ID: 17C65
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 6031786
zbMATH Keywords: CAR algebra
zbMATH Keywords: Cartan factor
zbMATH Keywords: JC-operator space
zbMATH Keywords: operator space ideal
zbMATH Keywords: reversibility
zbMATH Keywords: ternary ring of operators
zbMATH Keywords: universal TRO
reviewed by: Mixalis Anoussis
MaRDI profile type: Publication
OpenAlex ID: W2061121490
arXiv ID: 1007.1085
cites work: State space of C*-algebras
cites work: Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
cites work: Q4828515
cites work: Classification of JBW*-triple factors and applications.
cites work: Q4520854
cites work: Solution of the contractive projection problem
cites work: The Gelfand-Naimark theorem for \(JB^ *\)-triples
cites work: Q4942571
cites work: On the Structure and Tensor Products of JC-Algebras
cites work: Q5186181
cites work: Q4045220
cites work: A Generalization of C* -Algebras
cites work: Q4887825
cites work: Q3736359
cites work: A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces
cites work: Contractive projections on Jordan $C^*$-algebras and generalizations.
cites work: On JB\(^*\)-triples defined by fibre bundles
cites work: Completely 1-complemented subspaces of Schatten spaces
cites work: Classification of contractively complemented Hilbertian operator spaces
cites work: Contractive projections and operator spaces
cites work: Representation of contractively complemented Hilbertian operator spaces on the Fock space
cites work: Q4787522
cites work: Q4431278
cites work: Q4313489
cites work: Injectivity of Operator Spaces
cites work: Q4313492
cites work: Q4742013
cites work: COMPLETELY CONTRACTIVE PROJECTIONS ON C*-ALGEBRAS
cites work: A characterization of ternary rings of operators
DOI: 10.1007/S00209-010-0834-Y
description: scientific article; zbMATH DE number 6031786