[Banach] Abstract of a paper by Marek Cuth, Michal Doucha, and Przemyslaw Wojtaszczyk

This is an announcement for the paper "On the structure of Lipschitz-free spaces" by Marek Cuth, Michal Doucha, and Przemyslaw Wojtaszczyk.

Abstract: In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach 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 $F(M)$.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 54E35

Submitted from: marek.cuth@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1505.07209

or

http://arXiv.org/abs/1505.07209