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arXiv · 2112.03095

Schauder bases in Lipschitz free spaces over nets in Banach spaces

Petr Hájek·Rubén Medina
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Abstract

In the present note we give two explicit constructions (based on a retractional argument) of a Schauder basis for the Lipschitz free space $\mathcal{F}(N)$, over certain uniformly discrete metric spaces $N$. The first one applies to every net $N$ in a finite dimensional Banach space, leading to the basis constant independent of the dimension. The second one applies to grids in Banach spaces with an FDD. As a corollary, we obtain a retractional Schauder basis for the Lipschitz free space $\mathcal{F}(N)$ over a net $N$ in every Banach space $X$ with a Schauder basis containing a copy of $c_0$, as well as in every Banach space with a $c_0$-like FDD.

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Petr Hájek, Rubén Medina. 2021-12-06. Schauder bases in Lipschitz free spaces over nets in Banach spaces. https://arxiv.org/abs/2112.03095

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