On embeddings of finite subsets of ${\ell }_2$

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.

12 pages

References in corpus (1)

• Equilateral sets in finite-dimensional normed spaces

Cited by in corpus (2)

• There is no finitely isometric Krivine's theorem
• Isometric embeddings of a class of separable metric spaces into Banach spaces