Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 8 1 2024 01 26 Unbounded Order-to-Order Continuous Operators on Riesz Spaces 82 90 420 10.22128/gadm.2024.696.1094 EN Kazem Haghnejad Azar Department of Mathematics and Application Faculty of Sciences University of Mohaghegh Ardabili, Ardabil, Iran Mina Matin Department of Mathematics and Application Faculty of Sciences University of Mohaghegh Ardabili, Ardabil, Iran Sajjad Ghanizadeh Zare Department of Mathematics and Application Faculty of Sciences University of Mohaghegh Ardabili, Ardabil, Iran Journal Article 2023 08 04 ‎Let $E$ and $F$ be two Riesz spaces‎. ‎An operator $T \colon E\rightarrow F$ between two Riesz spaces is said to be‎ ‎unbounded order-to-order continuous whenever $x _\alpha \xrightarrow{uo}0$ in $E$ implies $Tx _\alpha \xrightarrow{o}0$ in $F$ for each net $(x_\alpha)\subseteq E$‎. ‎This paper aims to investigate several properties of a novel class of operators and their connections to established operator classifications‎. ‎Furthermore‎, ‎we introduce a new class of operators‎, ‎which we refer to as order-to-unbounded order continuous operators‎. ‎An operator $T \colon E\rightarrow F$ between two Riesz spaces is said to be‎ ‎order-to-unbounded order continuous (for short‎, ‎$ouo$-continuous)‎, ‎if $x _\alpha \xrightarrow{o}0$ in $E$ implies $Tx _\alpha \xrightarrow{uo}0$ in $F$ for each net $(x_\alpha)\subseteq E$‎. ‎In this manuscript‎, ‎we investigate the lattice properties of a certain class of objects and demonstrate that‎, ‎under certain conditions‎, ‎order continuity is equivalent to unbounded order-to-order continuity of operators on Riesz spaces‎. ‎Additionally‎, ‎we establish that the set of all unbounded order-to-order continuous linear functionals on a Riesz space $E$ forms a band of $E^\sim$. https://ansne.du.ac.ir/article_420_2ce946fbbf876e3400d86efce7b05e70.pdf