Conditioned square functions for noncommutative martingales

Details Conditioned square functions for noncommutative martingales Conditioned square functions for noncommutative martingales

2005-09-09

arxiv.org/abs/math/0509226v2

Annals of Probability 2007, Vol. 35, No. 3, 1039-1070

Mathematics

Operator Algebras

Published at http://dx.doi.org/10.1214/009117906000000656 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000656

We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative $L^p$-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948--995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.

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