Operator space structure of \(JC^*\)-triples and TROs. I
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 \(B(H)\).
scientific article; zbMATH DE number 6031786
scientific article