Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces
Abstract
Description
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 appear 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.
To appear in Indiana Univ. Math. J. 14 pages
To appear in Indiana Univ. Math. J. 14 pages