The Class of Demi-Order Norm Continuous Operators

Year 2023, Volume: 36 Issue: 4, 1693 - 1698, 01.12.2023

Gül Sinem Keleş , Birol Altın

https://doi.org/10.35378/gujs.1098503

Cited By: 1

Abstract

In this paper, we introduce the class of demi-order norm continuous operator on a normed Riesz space. We study the relationship between order-to-norm continuous operator and demi-order norm continuous operator. We also investigate some properties of the class of demi-order norm continuous operator, and it is given a characterization of a normed Riesz space with order continuous norm by the term of the demi-order norm continuous operator.

Keywords

Order continuous norm, Normed Riesz Space, Demi-order norm continuous operator

References

• [1] Petryshyn, W.V., “Construction of fixed points of demicompact mappings in Hilbert space”, Journal of Mathematical Analysis and Applications, 14(2): 276-284, (1966).
• [2] Krichen, B., O’Regan, D., “Weakly demicompact linear operators and axiomatic measures of weak noncompactness”, Mathematica Slovaca, 69(6): 1403-1412, (2019).
• [3] Benkhaled, H., Hajji, M., Jeribi, A., “On the class of Demi Dunford- Pettis Operators”, Rendiconti del Circolo Matematico di Palermo, Ser.2, 1-11, (2022).
• [4] Benkhaled, H., Elleuch, A., Jeribi, A., “The class of order weakly demicompact operators”, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A Matemáticas., 114(2): 1-8, (2020).
• [5] Jalili, A., Haghnejad, K., Moghimi, M., “Order-to-topology continuous operators”, Positivity, 25(2): 1-10, (2021).
• [6] Aliprantis, C.D., Burkinshaw, O., Positive Operators, 119, Berlin, (2006).