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arXiv · 1603.01391

Lipschitz-free spaces and Schur properties

Colin Petitjean
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Abstract

In this paper we study $\ell_1$-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 $\ell_1$-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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Colin Petitjean. 2016-03-04. Lipschitz-free spaces and Schur properties. https://arxiv.org/abs/1603.01391

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