Unbounded order-to-order continuous operators and order-to-unbounded order continuous operators on Riesz spaces Unbounded Order-to-Order Continuous Operators on Riesz Spaces
Department of Mathematics and Application Faculty of Sciences University of Mohaghegh Ardabili, Ardabil, Iran
10.22128/gadm.2024.696.1094
Abstract
Let E and F be two Riesz spaces. An operator T : E→ F between two Riesz spaces is said to be unbounded order-to-order continuous whenever x∝→ 0 in E implies Tx∝ → 0 in F for each net (x∝)⊆ 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 : E→ F rightarrow F between two Riesz spaces is said to beorder-to-unbounded order continuous (for short, ouo-continuous), if x∝→ 0 in E implies Tx∝ → 0 in F for each net (x∝)⊆ 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∼.
Haghnejad Azar, K., Matin, M., & Ghanizadeh Zare, S. (2023). Unbounded order-to-order continuous operators and order-to-unbounded order continuous operators on Riesz spaces Unbounded Order-to-Order Continuous Operators on Riesz Spaces. Global Analysis and Discrete Mathematics, 8(1), 105-115. doi: 10.22128/gadm.2024.696.1094
MLA
Kazem Haghnejad Azar; Mina Matin; Sajjad Ghanizadeh Zare. "Unbounded order-to-order continuous operators and order-to-unbounded order continuous operators on Riesz spaces Unbounded Order-to-Order Continuous Operators on Riesz Spaces". Global Analysis and Discrete Mathematics, 8, 1, 2023, 105-115. doi: 10.22128/gadm.2024.696.1094
HARVARD
Haghnejad Azar, K., Matin, M., Ghanizadeh Zare, S. (2023). 'Unbounded order-to-order continuous operators and order-to-unbounded order continuous operators on Riesz spaces Unbounded Order-to-Order Continuous Operators on Riesz Spaces', Global Analysis and Discrete Mathematics, 8(1), pp. 105-115. doi: 10.22128/gadm.2024.696.1094
VANCOUVER
Haghnejad Azar, K., Matin, M., Ghanizadeh Zare, S. Unbounded order-to-order continuous operators and order-to-unbounded order continuous operators on Riesz spaces Unbounded Order-to-Order Continuous Operators on Riesz Spaces. Global Analysis and Discrete Mathematics, 2023; 8(1): 105-115. doi: 10.22128/gadm.2024.696.1094
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