Universally reversible JC*-triples and operator spaces
Citation:
Leslie J. Bunce and Richard M. Timoney, Universally reversible JC*-triples and operator spaces, Journal of the London Mathematical Society, 88, 1, 2013, 271 - 293Download Item:
1209.6067.pdf (Published (author's copy) - Peer Reviewed) 364.0Kb
Abstract:
We prove that the vast majority of JC*-triples satisfy the condition of universal reversibility. Our characterisation is that a JC*-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW*-triples and of TROs (regarded as JC*-triples). We show that the distinct natural operator space structures on a universally reversible JC*-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.
Sponsor
Grant Number
Science Foundation Ireland (SFI)
11/RFP/MTH3187
Author's Homepage:
http://people.tcd.ie/rtimoneyDescription:
PUBLISHED
Author: TIMONEY, RICHARD
Type of material:
Journal ArticleSeries/Report no:
Journal of the London Mathematical Society88
1
Availability:
Full text availableKeywords:
Cartan factor, JC-operator space, operator space ideal, ternary ring of operators, universal TRO, tripotent, projectionSubject (TCD):
Jordan tripe systems , Operator spacesDOI:
http://dx.doi.org/10.1112/jlms/jdt016Licences: