Weak Banach-Saks property and Komlós’ theorem for preduals of JBW*-triples - Archive ouverte HAL Access content directly
Journal Articles Proceedings of the American Mathematical Society Year : 2016

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

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 L^1 , a subspace of a JBW ∗ ^* -triple predual contains ℓ 1 \ell _1 as soon as it contains uniform copies of ℓ 1 n \ell _1^n .

Dates and versions

hal-03491834 , version 1 (17-12-2021)

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Antonio Peralta, Hermann Pfitzner. Weak Banach-Saks property and Komlós’ theorem for preduals of JBW*-triples. Proceedings of the American Mathematical Society, 2016, 144 (11), pp.4723-4731. ⟨10.1090/proc/13250⟩. ⟨hal-03491834⟩
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