[Banach] Abstract of a paper by James Kilbane

This is an announcement for the paper “On embeddings of finite subsets of $\ell_2$” by James Kilbanehttps://arxiv.org/find/math/1/au:+Kilbane_J/0/1/0/all/0/1.

Abstract: We study finite subsets of $\ell_2$, 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 $\ell_2$ isometrically. The updated version contains acknowledgement that Theorem 3.1 has been proven previously in a paper of Shkarin.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.08971