DW-compact operators on Banach lattices

被引：0
|
作者：
Chen, Jin Xi [1 ]
Feng, Jingge [1 ]
机构：
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China
来源：
POSITIVITY | 2025年 / 29卷 / 01期
关键词：
Disjointly weakly compact set; <italic>DW</italic>-compact operator; <italic>AM</italic>-compact operator; Almost Dunford-Pettis operator; Banach lattice; DUNFORD-PETTIS SETS;
D O I：
10.1007/s11117-024-01106-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is devoted to the study of DW-compact operators, that is, those operators which map disjointly weakly compact sets in a Banach lattice onto relatively compact sets. We show that DW-compact operators are precisely the operators which are both Dunford-Pettis and AM-compact. As an application, Banach lattices with the property that every disjointly weakly compact set is a limited (resp. Dunford-Pettis) set, are characterized by using DW-compact operators.
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页数：15
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