Weak Banach-Saks property and Komlos theorem for preduals of\n JBW^*-triples

2015/05/20 by Antonio M. Peralta, Peralta, Antonio M., Hermann Pfitzner +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1505.05302

openalex publication_date 2015/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that the predual of a JBW^*-triple has the weak Banach-Saks\nproperty, that is, reflexive subspaces of a JBW^*-triple predual are\nsuper-reflexive. We also prove that JBW^*-triple preduals satisfy the\nKoml 'os property (which can be considered an abstract version of the weak law\nof large numbers). The results rely on two previous papers from which we infer\nthe fact that, like in the classical case of L¹, a subspace of a\nJBW^*-triple predual contains \ℓ₁ as soon as it contains uniform copies\nof \ℓ₁ⁿ.\n

Citations

• Banach embedding properties of non-commutative L^p-spaces

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