Banach-Saks index in spaces with symmetric basis

被引：1

作者：

Novikova, A. I. ^{[1
]}

Semenova, E. M. ^{[1
]}

Sukochev, F. A. ^{[2
]}

机构：

[1] Voronezh State Univ, Voronezh 394693, Russia

[2] Flinders Univ S Australia, Adelaide, SA, Australia

来源：

DOKLADY MATHEMATICS | 2008年 / 77卷 / 03期

基金：

澳大利亚研究理事会; 俄罗斯基础研究基金会;

关键词：

Banach Space; Dual Space; Standard Basis; Doklady Mathematic; Lorentz Space;

D O I：

10.1134/S1064562408030204

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Banach-Saks index of the separable part of the Marcinkiewicz spaces was calculated and estimated. A Banach space E of measurable functions on [0, 1] is called rearrangement invariant or symmetric. Kakutani proved that the uniform convexity of a space implies its Banach-Saks property. Baernstein constructed an example of a reflexive space with an unconditional basis that fails to have the Banach-Saks property. Banach and Saks proved that γ(Lp) = min(p, 2) and γ(lp) = p for all 1< p <∞.

引用

页码：396 / 397

页数：2

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