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
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页码：91 / 98
页数：8
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