Conditioned square functions for noncommutative martingales
Operator Algebras
2011-11-09 v2 Functional Analysis
Probability
Abstract
We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative -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.
Cite
@article{arxiv.math/0509226,
title = {Conditioned square functions for noncommutative martingales},
author = {Narcisse Randrianantoanina},
journal= {arXiv preprint arXiv:math/0509226},
year = {2011}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000656 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)