Multi-indexed $p$-orthogonal sums in non-commutative Lebesgue spaces
Javier Parcet
46L5205A18Khintchine inequalityMoebius inversion$p$-orthogonal sums
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.
Indiana University Mathematics Journal
2004
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10.1512/iumj.2004.53.2576
10.1512/iumj.2004.53.2576
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Indiana Univ. Math. J. 53 (2004) 1171 - 1188
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