Weak Banach-Saks property and Komlós’ theorem for preduals of JBW*-triples

Peralta, Antonio; Pfitzner, Hermann

doi:10.1090/proc/13250

Weak Banach-Saks property and Komlós’ theorem for preduals of JBW$^*$-triples
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Proc. Amer. Math. Soc. 144 (2016), 4723-4731 Request permission

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 Komlós 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 $\ell _1^n$.

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