Totally bounded sets in the absolute weak topology

被引：1

作者：

Ardakani, Halimeh ^{[1
]}

Chen, Jin Xi ^{[2
]}

机构：

[1] Payame Noor Univ, Dept Math, POB 19395-3697, Tehran, Iran

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 545卷 / 02期

关键词：

Almost L-set; PL-compact operator; Almost Dunford-Pettis operator; Banach lattice; |sigma; |(E; E ' )-totally bounded set; DUNFORD-PETTIS SETS; OPERATORS;

D O I：

10.1016/j.jmaa.2024.129164

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, almost Dunford-Pettis operators with ranges in c0 are used to identify totally bounded sets in the absolute weak topology. That is, a bounded subset A of a Banach lattice E is sigma(E, E')-totally bounded if and only if T(A) C c0 is relatively compact for every almost Dunford-Pettis operator T : E-* c0. As an application, we show that for two Banach lattices E and F every positive operator from E to F dominated by a PL-compact operator is PL-compact if and only if either the norm of E' is order continuous or every order interval in F is sigma(F, F')-totally bounded. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：14

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[3]

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