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Winter 2000 An inequality for $p$-orthogonal sums in non-commutative $L_{p}$
Gilles Pisier
Author Affiliations +
Illinois J. Math. 44(4): 901-923 (Winter 2000). DOI: 10.1215/ijm/1255984700

Abstract

We give an alternate proof of one of the inequalities proved recently for martingales (= sums of martingale differences) in a non-commutative $L_{p}$-space, with $1 \lt p \lt \infty$, by Q. Xu and the author. This new approach is restricted to $p$ an even integer, but it yields a constant which is $O(p)$ when $p \rightarrow \infty$ and it applies to a much more general kind of sum which we call $p$-orthogonal. We use mainly combinatorial tools, namely the Möbius inversion formula for the lattice of partitions of a $p$-element set.

Citation

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Gilles Pisier. "An inequality for $p$-orthogonal sums in non-commutative $L_{p}$." Illinois J. Math. 44 (4) 901 - 923, Winter 2000. https://doi.org/10.1215/ijm/1255984700

Information

Published: Winter 2000
First available in Project Euclid: 19 October 2009

zbMATH: 0976.60016
MathSciNet: MR1804311
Digital Object Identifier: 10.1215/ijm/1255984700

Subjects:
Primary: 46L53
Secondary: 60B99 , 60G46 , 60G48

Rights: Copyright © 2000 University of Illinois at Urbana-Champaign

Vol.44 • No. 4 • Winter 2000
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