Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682215120240101Almost order-weakly compact operators on Banach lattices353360761910.22075/ijnaa.2022.26958.3462ENMohammad PaziraDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranMina MatinDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranKazem Haghnejad AzarDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranAli AbadiDepartment of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranJournal Article20220423A 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.https://ijnaa.semnan.ac.ir/article_7619_e4b6f12904e90faf55bda2772fdad553.pdf