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

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.