Noncommutative Burkholder/Rosenthal inequalities

• 成果类型: Article
• 署名作者: Junge, M; Xu, QH
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Universite Marie et Louis Pasteur
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 948-995
• 关键词: generalized conditional expectations; martingale inequalities; vonneumann-algebras; lp-spaces; l-p; interpolation; khintchine; PRODUCTS

摘要

We investigate martingale inequalities in noncommutative L-p-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.