This is an announcement for the paper “There is no finitely isometric Krivine's theorem” by James Kilbanehttps://arxiv.org/find/math/1/au:+Kilbane_J/0/1/0/all/0/1, Mikhail I. Ostrovskhttps://arxiv.org/find/math/1/au:+Ostrovskii_M/0/1/0/all/0/1.

Abstract: We prove that for every $p\in (1, \infty)$, $p\neq 2$, 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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.01570