Tree Martingales in Noncommutative Probability Spaces

被引：0
作者：
Ghadir Sadeghi
机构：
[1] Hakim Sabzevari University,Department of Mathematics and Computer Sciences
[2] Ferdowsi University of Mashhad,Center of Excellence in Analysis on Algebraic Structures (CEAAS)
来源：
Complex Analysis and Operator Theory | 2020年 / 14卷
关键词：
Noncommutative probability space; Symmetric operator spaces; Tree martingale; Burkholder–Gundy inequalities; Primary 46L53; Secondary 46L10; 47A30; 60G46;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce the notion of a tree martingale in a noncommutative probability space and prove the Burkholder–Gundy inequalities for tree martingales in symmetric operator spaces. In particular, we establish some inequalities in this setting via an approach based on the concept of generalized singular valued functions of noncommutative random valuables.
引用
收藏
相关论文
共 15 条
  • [1] Fack T(1986)Generalized Pac. J. Math. 123 269-300
  • [2] Kosaki H(2012)-numbers of Arch. Math. 98 87-97
  • [3] Jiao Y(1997)-measurable operators Commun. Math. Phys. 189 667-698
  • [4] Pisier G(1973)Martingale inequalities in noncommutative symmetric spaces Trans. Am. Math. Soc. 185 345-370
  • [5] Xu Q(2014)Non-commutative martingale inequalities Illinois J. Math. 58 561-575
  • [6] Gosselin J(2016)Almost everywhere convergence of vilenkin-fourier series Rocky Mount. J. Math. 46 309-323
  • [7] Sadeghi Gh(2019)Noncommutative martingale concentration inequalities Adv. Oper. Theory 4 784-792
  • [8] Moslehian MS(1976)Inequalities for sums of random variables in noncommutative probability spaces Anal. Math. 189 65-76
  • [9] Sadeghi Gh(1994)A trick for investigation of near-martingales in quantum probability spaces Lect. Notes Math. 1568 1-563
  • [10] Moslehian MS(1991)Pointwise convergence of expansions with respect to certain product systems Math. Proc. Cambridge Philos. Soc. 109 541-undefined
12