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International Journal of Nonlinear Analysis and Applications، جلد ۱۶، شماره ۳، صفحات ۱۶۷-۱۷۴
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عنوان انگلیسی $tilde{O}$rder-norm continuous operators and $tilde{o}$rder weakly compact operators
چکیده انگلیسی مقاله 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 $x_alphaxrightarrow{Fo}0$ 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 $Asubseteq E$. In this manuscript, we examine various properties of this class of operators and explore their connections with $tilde{o}$rder-norm continuous operators.
کلیدواژه‌های انگلیسی مقاله Vector lattice,property $(F)$,$tilde{o}$-convergence,order-to-norm continuous operator,$tilde{o}$rder-norm continuous operator,$tilde{o}$rder weakly compact
نویسندگان مقاله Sajjad Ghanizadeh Zare |
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Kazem Haghnejad Azar |
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Mina Matin |
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Somayeh Hazrati |
Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

نشانی اینترنتی https://ijnaa.semnan.ac.ir/article_8617_1236d4755a31b082b72642eba35315cb.pdf
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