Weakly compact operators on Jordan triples. (English) Zbl 0627.46061

We obtain some criteria for the weak compactness of bounded operators on \(JB^ *\)-triples, extending the results of Akemann et al. and Jarchow for \(C^ *\)-algebras. From this we derive some Banach space properties for \(JB^ *\)-triples.


46H70 Nonassociative topological algebras
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
17C65 Jordan structures on Banach spaces and algebras
46L70 Nonassociative selfadjoint operator algebras
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