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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 | ||
| تاریخ دریافت: 03 اردیبهشت 1401، تاریخ بازنگری: 13 تیر 1401، تاریخ پذیرش: 15 تیر 1401 | ||
| 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 | ||
| مراجع | ||
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