Abstract
We investigate martingale inequalities in noncommutative Lp-spaces associated with a von Neumann algebra equipped with a faithful normal state. We prove the noncommutative analogue of the classical Burkholder inequality on the conditioned (or little) square function and extend the noncommutative Burkholder-Gundy inequalities from Comm. Math. Phys. 189 (1997) 667-698 to this nontracial setting. We include several related results.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 948-995 |
| Number of pages | 48 |
| Journal | Annals of Probability |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2003 |
Keywords
- (Noncommutative) martingale inequalities
- (noncommutative) Burkholder inequality
- (noncommutative) Rosenthal inequality
- Noncommutative L spaces
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty