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

TL;DR

This paper systematically investigates the operator space structures of JC*-triples by introducing universal TROs, providing explicit descriptions and characterizations across various examples, including Cartan factors.

Contribution

It introduces universal TROs and the concept of reversibility to describe all operator space structures of JC*-triples, extending understanding of their structure.

Findings

Explicit descriptions of operator space structures of Cartan factors.

Characterizations of universal TROs over diverse examples.

Development of a framework for classifying JC*-triples by their operator space structures.

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.