Almost order-weakly compact operators on Banach lattices

Document Type : Research Paper


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



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.


Articles in Press, Corrected Proof
Available Online from 03 April 2023
  • Receive Date: 23 April 2022
  • Revise Date: 04 July 2022
  • Accept Date: 06 July 2022
  • First Publish Date: 03 April 2023