An inequality for p-orthogonal sums in non-commutative L-p
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abstract
We give an alternate proof of one of the inequalities proved recently for martingales (= sums of martingale differences) in a non-commutative Lp-space, with 1 < p < , 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 and it applies to a much more general kind of sum which we call p-orthogonal. We use mainly combinatorial tools, namely the Mbius inversion formula for the lattice of partitions of a p-element set.
