IUMJ

Title: Multi-indexed $p$-orthogonal sums in non-commutative Lebesgue spaces

Authors: Javier Parcet

Issue: Volume 53 (2004), Issue 4, 1171-1188

Abstract:

In this paper we extend a recent Pisier's inequality for $p$-orthogonal sums in non-commutative Lebesgue spaces. To that purpose, we generalize the notion of $p$-orthogonality to the class of multi-indexed families of operators. This kind of families appears naturally in certain non-commutative Khintchine type inequalities associated with free groups. Other $p$-orthogonal families are given by the homogeneous operator-valued polynomials in the Rademacher variables or the multi-indexed martingale difference sequences. As in Pisier's result, our tools are mainly combinatorial.