This is an announcement for the paper "Weak Banach-Saks property and Koml'os' theorem for preduals of JBW$^*$-triples" by Antonio M. Peralta and Hermann Pfitzner.
Abstract: We show that the predual of a JBW$^*$-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW$^*$-triple predual are super-reflexive. We also prove that JBW$^*$-triple preduals satisfy the Koml'os property (which can be considered an abstract version of the weak law of large numbers). The results rely on two previous papers from which we infer the fact that, like in the classical case of $L^1$, a subspace of a JBW$^*$-triple predual contains $\ell_1$ as soon as it contains uniform copies of $\ell_1^n$.
Archive classification: math.OA math.FA
Submitted from: aperalta@ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.05302
or