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$\tilde{O}$rder-norm continuous operators and $\tilde{o}$rder weakly compact operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 16، شماره 3، خرداد 2025، صفحه 167-174 اصل مقاله (377.87 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32603.4858 | ||
| نویسندگان | ||
| Sajjad Ghanizadeh Zare؛ Kazem Haghnejad Azar* ؛ Mina Matin؛ Somayeh Hazrati | ||
| Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran | ||
| تاریخ دریافت: 16 آذر 1402، تاریخ پذیرش: 24 بهمن 1402 | ||
| چکیده | ||
| Let $E$ be a sublattice of a vector lattice $F$. A continuous operator $T$ from $E$ into a normed vector space $X$ is said to be $\tilde{o}$rder-norm continuous if $x_\alpha\xrightarrow{Fo}0$ implies $T(x_\alpha)\xrightarrow{\Vert.\Vert}0$ for every $(x_{\alpha})_{\alpha \in A}\subseteq E$. This paper aims to investigate the properties of this new class of operators and explore their relationships with existing classifications of operators. We introduce a new class of operators called $\tilde{o}$rder weakly compact operators. A continuous operator $T: E \rightarrow X $ is considered $\tilde{o}$rder weakly compact if $ T(A) $ in $X$ is a relatively weakly compact set for every $Fo$-bounded $A\subseteq E$. In this manuscript, we examine various properties of this class of operators and explore their connections with $\tilde{o}$rder-norm continuous operators. | ||
| کلیدواژه‌ها | ||
| Vector lattice؛ property $(F)$؛ $\tilde{o}$-convergence؛ order-to-norm continuous operator؛ $\tilde{o}$rder-norm continuous operator؛ $\tilde{o}$rder weakly compact | ||
| مراجع | ||
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