Lipschitz-free spaces and Schur properties

2016/03/04 by Petitjean, Colin · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1603.01391

Abstract

In this paper we study ℓ₁-like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper metric space linearly embeds into an ℓ₁-sum of finite dimensional subspaces of itself. We also give a sufficient condition for a Lipschitz-free space to have the Schur property, the 1-Schur property and the 1-strong Schur property respectively. We finish by studying those properties on a new family of examples, namely the Lipschitz-free spaces over metric spaces originating from p-Banach spaces, for p in (0,1).

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• Lipschitz free p-spaces for 0
• Quantitative Schur property and measures of weak non-compactness

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