On embeddings of finite subsets of $\ell_2$
Functional Analysis
2016-09-30 v2 Metric Geometry
Abstract
We study finite subsets of , 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 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