Almost Dunford-Pettis sets in Banach lattices

被引：25

作者：

Bouras, Khalid ^{[1
]}

机构：

[1] Univ Ibn Tofail, Fac Sci, Dept Mathemat, BP 133, Kenitra, Morocco

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2013年 / 62卷 / 02期

关键词：

Almost Dunford-Pettis set; Relatively weakly compact sets; L-weakly compact sets; Weak Dunford-Pettis property; KB-space; Positive Schur property;

D O I：

10.1007/s12215-013-0105-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study the class of almost Dunford-Pettis sets in Banach lattices. It also discusses some of the consequences derived from this study. As an application, we characterize Banach lattices whose relatively weakly compact sets are almost Dunford-Pettis sets. Also, we establish some necessary and sufficient conditions on which an almost Dunford-Pettis set is L-weakly compact (respectively, relatively weakly compact). In particular, we characterize Banach lattices under which almost Dunford-Pettis sets in the topological dual of a Banach lattice coincide with that of L-weakly compact (respectively, relatively weakly compact) sets. As a consequences we derive some results.

引用

页码：227 / 236

页数：10

共 8 条

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