This is an announcement for the paper “Some remarks on the structure of Lipschitz-free spaces” by Petr Hájekhttp://arxiv.org/find/math/1/au:+Hajek_P/0/1/0/all/0/1, Matěj Novotnýhttp://arxiv.org/find/math/1/au:+Novotny_M/0/1/0/all/0/1.
Abstract: We give several structural results concerning the Lipschitz-free spaces $F(M)$ where $M$ is a metric space. We show that $F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=$dens$(M)$. If $\mathcal{N}$ is the net in a finite dimensional Banach space $X$, we show that $F(\mathcal{N})$ is isomorphic to its square. If $X$ contains a complemented copy of $\ell_p, c_0$ then $F(\mathcal{N})$ is isomorphic to its $\ell_1$-sum. Finally, we prove that for all $X\equiv C(K)$ spaces $F(\mathcal{N})$ are mutually isomorphic spaces with a Schauder basis.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.03926