This is an announcement for the paper "On Dvoretzky's theorem for subspaces of $L_p$" by Grigoris Paouris and Petros Valettas.

Abstract: We prove that for any $p > 2$ and every $n$-dimensional subspace $X$ of $L_p$, the Euclidean space $\ell_2^k$ can be $(1 + \varepsilon)$-embedded into $X$ with $k \geq c_p \min{\varepsilon^2 n, (\varepsilon n)^{2/p} }$, where $c_p > 0$ is a constant depending only on $p$.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 46B07, 46B09

Remarks: 20 pages

Submitted from: valettasp@missouri.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1510.07289

or

http://arXiv.org/abs/1510.07289