Cesaro mean convergence of martingale differences in rearrangement invariant spaces

被引：16

作者：

Astashkin, Sergey V. ^{[1
]}

Kalton, Nigel ^{[2
]}

Sukochev, Fyodor A. ^{[3
]}

机构：

[1] Samara State Univ, Dept Math & Mech, Samara 443086, Russia

[2] Univ Columbia Missouri, Dept Math, Columbia, MO USA

[3] Flinders Univ S Australia, Sch Informat & Engn, Bedford Pk, SA 5042, Australia

来源：

POSITIVITY | 2008年 / 12卷 / 03期

基金：

美国国家科学基金会;

关键词：

r.i. function spaces; Banach-saks property; martingale differences; weak compactness;

D O I：

10.1007/s11117-007-2146-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the class of r.i. spaces in which Cesaro means of any weakly null martingale difference sequence is strongly null. This property is related to the Banach-Saks property. We show that in classical (separable) r.i. spaces (such as Orlicz, Lorentz and Marcinkiewicz spaces) these properties coincide but this is no longer true for general r.i. spaces. We locate also a class of r.i. spaces having this property where an analogue of the classical Dunford-Pettis characterization of relatively weakly compact subsets in L(1) holds.

引用

页码：387 / 406

页数：20

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