KB-OPERATORS ON BANACH LATTICES AND THEIR RELATIONSHIPS WITH DUNFORD-PETTIS AND ORDER WEAKLY COMPACT OPERATORS

被引：0

作者：

Bahramnezhad, Akbar ^{[1
]}

Azar, Kazem Haghnejad ^{[1
]}

机构：

[1] Univ Mohaghegh Ardabili, Dept Math, Ardebil, Iran

来源：

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS | 2018年 / 80卷 / 02期

关键词：

Banach lattice; KB-operator; WKB-operator; KB-space; b-weakly compact operator;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Aqzzouz, Moussa and Hmichane proved that an operator T from a Banach lattice E into a Banach space X is b-weakly compact if and only if {T-x}(n) is norm convergent for every positive increasing sequence {x(n)}(n) of the closed unit ball B-E of E. In the present paper, we introduce and study new classes of operators that we call KB operators and W KB-operators. A continuous operator T from a Banach lattice E into a Banach space X is said to be KB-operator (respectively, W KB-operator) if {Tx(n)}(n) has a norm (respectively, weak) convergent subsequence in X for every positive increasing sequence {x(n)}(n) in the closed unit ball B-E of E. We investigate the relationships between KB-operators (respectively, W KB-operators) and some other operators on Banach lattices spacial their relationships with Dunford-Pettis and order weakly compact operators.

引用

页码：91 / 98

页数：8

共 48 条

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