This is an announcement for the paper "Martingale inequalities and operator space structures on $L_p$" by Gilles Pisier.

Abstract: We describe a new operator space structure on $L_p$ when $p$ is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's martingale inequalities have a very natural form:\ the span of the Rademacher functions is completely isomorphic to the operator Hilbert space $OH$, and the square function of a martingale difference sequence $d_n$ is $\Sigma \ d_n\otimes \bar d_n$. Various inequalities from harmonic analysis are also considered in the same operator valued framework. Moreover, the new operator space structure also makes sense for non commutative $L_p$-spaces with analogous results.

Archive classification: math.OA math.FA math.PR

Submitted from: pisier@math.jussieu.fr

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

http://front.math.ucdavis.edu/1209.1071

or

http://arXiv.org/abs/1209.1071