International Journal of Nonlinear Analysis and Applications

Almost order-weakly compact operators on Banach lattices

Document Type : Research Paper

Authors

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

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 1
January 2024
Pages 353-360
  • Receive Date: 23 April 2022
  • Revise Date: 04 July 2022
  • Accept Date: 06 July 2022