On embeddings of finite subsets of $\ell_2$
  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. 
James Kilbane
math.FA math.MG