%0 Journal Article
%T Almost order-weakly compact operators on Banach lattices
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Pazira, Mohammad
%A Matin, Mina
%A Haghnejad Azar, Kazem
%A Abadi, Ali
%D 2024
%\ 01/01/2024
%V 15
%N 1
%P 353-360
%! Almost order-weakly compact operators on Banach lattices
%K almost order bounded
%K weakly compact
%K order weakly compact
%K almost order-weakly compact
%R 10.22075/ijnaa.2022.26958.3462
%X 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.
%U https://ijnaa.semnan.ac.ir/article_7619_e4b6f12904e90faf55bda2772fdad553.pdf