Some characterizations of almost limited operators

被引：15

作者：

Elbour, Aziz ^{[1
]}

机构：

[1] Univ Moulay Ismail, Fac Sci & Tech, Dept Math, BP 509, Errachidia, Morocco

来源：

POSITIVITY | 2017年 / 21卷 / 03期

关键词：

Almost limited operator; Almost Dunford-Pettis operator; Limited operator; Order weakly compact operator; Almost limited set; Banach lattice; BANACH-LATTICES; DUNFORD-PETTIS;

D O I：

10.1007/s11117-016-0437-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator T : X -> E from a Banach space X into a sigma-Dedekind complete Banach lattice E is almost limited if and only if parallel to T* (f(n))parallel to -> 0 for every positive weak* null sequence (f(n)) of E*. Moreover, we present some interesting connections between almost limited, almost Dunford-Pettis and limited operators.

引用

页码：865 / 874

页数：10

共 12 条

[1]

Aliprantis C. D., 2006, POSITIVE OPERATORS

[2] Some characterizations of almost Dunford-Pettis operators and applications [J].