The Banach-Saks property in rearrangement invariant spaces

被引：27

作者：

Dodds, PG ^{[1
]}

Semenov, EM

Sukochev, FA

机构：

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

[2] Voronezh State Univ, Dept Math, Voronezh 394693, Russia

来源：

STUDIA MATHEMATICA | 2004年 / 162卷 / 03期

关键词：

D O I：

10.4064/sm162-3-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the BanachSaks property.

引用

页码：263 / 294

页数：32

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