Johnson-Schechtman inequalities for noncommutative martingales

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• 作者：Yong Jiao^a ; ¹ ; ^{jiaoyong@csu.edu.cn} ; Fedor Sukochev^b ; ^{f.sukochev@unsw.edu.au} ; Dmitriy Zanin^b ; ^{d.zanin@unsw.edu.au} ; Dejian Zhou^a ; ^{zhoudejian@csu.edu.cn}
• 关键词：primary ; 46L52 ; 46L53 ; 47A30 ; secondary ; 60G42
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：272
• 期：3
• 页码：976-1016
• 全文大小：607 K
• 卷排序：272

文摘

In this paper we study Johnson–Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space E(M)E(M) of a finite von Neumann algebra MM without making any assumption on the Boyd indices of E  . We show that we can obtain Johnson–Schechtman inequalities for arbitrary martingale difference sequences and that, in contrast with the classical case of independent random variables or the noncommutative case of freely independent random variables, the inequalities are one-sided except when E=L2(0,1)E=L2(0,1). As an application, we partly resolve a problem stated by Randrianantoanina and Wu in [46]. We also show that we can obtain sharp Φ-moment analogues for Orlicz functions satisfying p-convexity and q  -concavity for 1≤p≤21≤p≤2, q=2q=2 and p=2p=2, 2<q<∞2<q<∞. This is new even for the classical case. We also extend and strengthen the noncommutative Burkholder–Gundy inequalities in symmetric spaces and in the Φ-moment case.