Document Type : Research Paper

Authors

• Mohammad Pazira
• Mina Matin
• Kazem Haghnejad Azar
• Ali Abadi

Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

A continuous operator $T$ between two Banach lattices $E$ and     $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$,  $T(A)$ is a relatively weakly compact subset of $F$. We show that the positive operator $T$ from  $E$ into a  Dedekind complete Banach lattice $F$  is almost order-weakly compact iff  $T(x_n) \xrightarrow{\|.\|}0$ in $F$ for each disjoint almost order bounded sequence $\{x_n\}$ in $E$. In this manuscript, we study some properties of this class of operators and its relationships with the others known classes of operators.

Keywords

• almost order bounded
• weakly compact
• order weakly compact
• almost order-weakly compact