Almost limited sets in Banach lattices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Chen, Jin Xi^1,2  Chen, Zi Li²  Ji, Guo Xing¹ 

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

[2] Southwest Jiaotong Univ, Dept Math, Chengdu 610031, Peoples R China

关键词: Almost limited set;    The wDP* property;    Almost Dunford-Pettis operator;    Positive Schur property;    Banach lattice;   

DOI  :  10.1016/j.jmaa.2013.10.085

来源: Elsevier

【 摘 要 】

We introduce and study the class of almost limited sets in Banach lattices, that is, sets on which every disjoint weak* null sequence of functionals converges uniformly to zero. It is established that a Banach lattice has order continuous norm if and only if almost limited sets and L-weakly compact sets coincide. In particular, in terms of almost Dunford-Pettis operators into c(0), we give an operator characterization of those sigma-Dedekind complete Banach lattices whose relatively weakly compact sets are almost limited, that is, for a sigma-Dedekind Banach lattice E, every relatively weakly compact set in E is almost limited if and only if every continuous linear operator T : E -> c(0) is an almost Dunford-Pettis operator. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free