Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces

Details Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces

2003-12-13

arxiv.org/abs/math/0312275v2

Indiana Univ. Math. J. 53 (2004), 1171-1188.

Mathematics

Operator Algebras

To appear in Indiana Univ. Math. J. 14 pages

Scientific paper

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.

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