Almost order-weakly compact operators on Banach lattices

	Almost order-weakly compact operators on Banach lattices
International Journal of Nonlinear Analysis and Applications
مقاله 352، دوره 15، شماره 1، فروردین 2024، صفحه 353-360 اصل مقاله (359.15 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26958.3462
نویسندگان
Mohammad Pazira؛ Mina Matin؛ Kazem Haghnejad Azar^* ؛ Ali Abadi
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
چکیده
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.
کلیدواژه‌ها
almost order bounded؛ weakly compact؛ order weakly compact؛ almost order-weakly compact
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