Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Richard J. Smith; Filip Talimdjioski

Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property

Functional Analysis 2022-06-13 v1

Authors: Richard J. Smith , Filip Talimdjioski

Abstract

Let $\|\cdot\|$ be a norm on $\mathbb{R}^N$ and let $M$ be a closed $C^1$ -submanifold of $\mathbb{R}^N$ . Consider the pointed metric space $(M,d)$ , where $d$ is the metric given by $d(x,y)=\|x-y\|$ , $x,y\in M$ . Then the Lipschitz-free space $\mathcal{F}(M)$ has the Metric Approximation Property.

Keywords

lipschitz-free space metric approximation property c^1-submanifold normed space pointed metric space

Cite

@article{arxiv.2206.04953,
  title  = {Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property},
  author = {Richard J. Smith and Filip Talimdjioski},
  journal= {arXiv preprint arXiv:2206.04953},
  year   = {2022}
}

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19 pages

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