$\tilde{O}$rder-norm continuous operators and $\tilde{o}$rder weakly compact operators

Document Type : Research Paper


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



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.


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Articles in Press, Corrected Proof
Available Online from 17 March 2024
  • Receive Date: 07 December 2023
  • Accept Date: 13 February 2024