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arXiv · 2202.08032

Schauder basis in Lipschitz free spaces over nets of $\mathcal{L}_\infty$-spaces

Petr Hájek·Rubén Medina
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Abstract

In the present note we give a construction (based on a retractional argument) of a Schauder basis for the Lipschitz free space $\mathcal{F}(N)$, over a net $N$ in any separable infinite dimensional $\mathcal{L}_\infty$-space $X$. In particular, this yields the first example of an infinite dimensional Banach space $X$ not containing $c_0$ with such a property.

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Petr Hájek, Rubén Medina. 2022-02-16. Schauder basis in Lipschitz free spaces over nets of $\mathcal{L}_\infty$-spaces. https://arxiv.org/abs/2202.08032

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