There is no finitely isometric Krivine's theorem

Abstract

We prove that for every $p\in (1,\infty )$, $p\ne 2$, there exist a Banach space $X$ isomorphic to ${\ell }_p$ and a finite subset $U$ in ${\ell }_p$, such that $U$ is not isometric to a subset of $X$. This result shows that the finite isometric version of the Krivine theorem (which would be a strengthening of the Krivine theorem (1976)) does not hold.

References in corpus (1)

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