Abstract of a paper by Petr Hájek, Matěj Novotný
This is an announcement for the paper “Some remarks on the structure of Lipschitz-free spaces” by Petr Hájek<http://arxiv.org/find/math/1/au:+Hajek_P/0/1/0/all/0/1>, Matěj Novotný<http://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
participants (1)
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Bentuo Zheng (bzheng)