Complemented copies of \ℓ₁ in spaces of vector valued measures and\n applications

1995/10/31 by Narcisse Randrianantoanina, Randrianantoanina, Narcisse
Computer Science · Mathematics · #46E #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.math/9511206

openalex publication_date 1995/10/31 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let X be a Banach space and (\Ω,\Σ) be a measure space. We\nprovide a characterization of sequences in the space of X-valued countably\nadditive measures on \Ω,\Σ) of bounded variation that generate\ncomplemented copies of \ℓ₁. As application, we prove that if a dual Banach\nspace E^* has Pe l czy 'nski's property (V*) then so does the space of\nE^*-valued countably additive measures with bounded variation. Another\napplication, we show that for a Banach space X, the space \ℓ_\∞(X)\ncontains a complemented copy of \ℓ₁ if and only if X contains all\n\ℓ₁ⁿ uniformly complemented.\n

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