Operator space structure of JC*-triples and TROs, I

Bunce, L. J., Feely, B. and Timoney, R. M. (2012) Operator space structure of JC*-triples and TROs, I. Mathematische Zeitschrift, 270 (3-4). pp. 961-982. ISSN 0025-5874 doi: 10.1007/s00209-010-0834-y

Abstract/Summary

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension