Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$

Abstract

Using a recent result of Batson, Spielman and Srivastava, We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even integer, needed to almost isometrically contain all $k$-dimensional subspaces of $L_p$.