Positively limited sets in Banach lattices

被引：10

作者：

Ardakani, Halimeh ^{[1
]}

Chen, Jin Xi ^{[2
]}

机构：

[1] Payame Noor Univ, Dept Math, Tehran, Iran

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 526卷 / 01期

关键词：

Positively limited set; Almost limited set; Positive GP property; Positive BD property; Banach lattice; DUNFORD-PETTIS SETS; PROPERTY; OPERATORS; SPACES;

D O I：

10.1016/j.jmaa.2023.127220

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and study the class of positively limited sets in Banach lattices, that is, sets on which every weak* null sequence of positive functionals converges uniformly to zero. Moreover the relationships between the class of positively limited sets and other known classes of sets such as almost limited sets and (weakly) compact sets are discussed. Some properties of Banach lattices can be characterized in terms of positively limited sets.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：12

共 23 条

[1]

Aliprantis C.D., 2006, Positive operators, DOI DOI 10.1007/978-1-4020-5008-4

[2]

ALIPRANTIS CD, 1978, PURE APPL MATH, V76

[3] DUNFORD-PETTIS SETS IN THE SPACE OF BOCHNER INTEGRABLE FUNCTIONS [J].