R. Smith

will speak on

Lipschitz-free spaces and the metric approximation property

Time: 4:00PM
Date: Tue 30th September 2014
Location: [map]

Abstract: Given a metric space $M$ with distinguished point $0$, the Lipschitz-free space $mathcal F(M)$ is the natural predual of the space of Lipschitz functions that vanish at $0$ (endowed with the Lipschitz norm). The study of these spaces is an emerging area of research. Despite their elementary definition, the linear structure of the spaces $mathcal F(M)$ is still relatively poorly understood: in many cases it is not known whether $mathcal F(M)$ has the approximation property, a finite-dimensional decomposition or a Schauder basis. In this talk we show that for certain subsets $M$ of $mathbb R^N$ (such as all finite-dimensional compact convex sets), the Lipschitz-free space $mathcal F(M)$ has the metric approximation property, independent of the choice of norm on $mathbb R^N$. This contrasts with the fact, proved by Godefroy and Ozawa, that there exist infinite-dimensional compact convex sets $M$ such that $mathcal F(M)$ does not have the approximation property.

(This talk is part of the Analysis series.)

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