, Volume 270, Issue 3-4, pp 961-982

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

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Abstract

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

The work of the B. Feely and R.M. Timoney was supported by the Science Foundation Ireland under grant 05/RFP/MAT0033.