Abstract of a paper by Eva Pernecka and Richard J. Smith
This is an announcement for the paper "The Metric Approximation Property and Lipschitz-Free Spaces over Subsets of $\mathbb{R}^N$" by Eva Pernecka and Richard J. Smith. Abstract: We prove that for certain subsets $M \subseteq \mathbb{R}^N$, $N \geqslant 1$, the Lipschitz-free space $\mathcal{F}(M)$ has the metric approximation property (MAP), with respect to any norm on $\mathbb{R}^N$. In particular, $\mathcal{F}(M)$ has the MAP whenever $M$ is a finite-dimensional compact convex set. This should be compared with a recent result of Godefroy and Ozawa, who showed that there exists a compact convex subset $M$ of a separable Banach space, for which $\mathcal{F}(M)$ fails the approximation property. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B28 Submitted from: richard.smith@maths.ucd.ie The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1501.07036 or http://arXiv.org/abs/1501.07036
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alspach@math.okstate.edu