English

On embeddings of finite subsets of $\ell_2$

Functional Analysis 2016-09-30 v2 Metric Geometry

Abstract

We study finite subsets of 2\ell_2, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains every finite subset of 2\ell_2 isometrically. The updated version contains acknowledgement that Theorem 3.1 has been proven previously in a paper of Shkarin.

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Cite

@article{arxiv.1609.08971,
  title  = {On embeddings of finite subsets of $\ell_2$},
  author = {James Kilbane},
  journal= {arXiv preprint arXiv:1609.08971},
  year   = {2016}
}

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12 pages