[Banach] Abstract of a paper by Jop Briet, Assaf Naor, and Oded Regev

This is an announcement for the paper "Locally decodable codes and the failure of cotype for projective tensor products" by Jop Briet, Assaf Naor, and Oded Regev.

Abstract: It is shown that for every $p\in (1,\infty)$ there exists a Banach space $X$ of finite cotype such that the projective tensor product $\ell_p\tp X$ fails to have finite cotype. More generally, if $p_1,p_2,p_3\in (1,\infty)$ satisfy $\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\le 1$ then $\ell_{p_1}\tp\ell_{p_2}\tp\ell_{p_3}$ does not have finite cotype. This is a proved via a connection to the theory of locally decodable codes.

Archive classification: math.FA cs.CC

Submitted from: odedr@cs.tau.ac.il

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

http://front.math.ucdavis.edu/1208.0539

or

http://arXiv.org/abs/1208.0539