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arXiv · 1505.07209

On the structure of Lipschitz-free spaces

Marek Cuth·Michal Doucha·Przemyslaw Wojtaszczyk
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Abstract

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of $\ell_1$. This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space $K$ such that $F(K)$ is not isomorphic to a subspace of $L_1$ and we show that whenever $M$ is a subset of $R^n$, then $F(M)$ is weakly sequentially complete; in particular, $c_0$ does not embed into $F(M)$.

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Marek Cuth, Michal Doucha, Przemyslaw Wojtaszczyk. 2015-05-27. On the structure of Lipschitz-free spaces. https://doi.org/10.1090/proc%2F13019

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