English

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 LpL^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.

Keywords

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)