## On unbounded order continuous operators

Turkish Journal of Mathematics, vol.46, no.8, pp.3391-3399, 2022 (SCI-Expanded) • Publication Type: Article / Article
• Volume: 46 Issue: 8
• Publication Date: 2022
• Doi Number: 10.55730/1300-0098.3339
• Journal Name: Turkish Journal of Mathematics
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
• Page Numbers: pp.3391-3399
• Keywords: Order convergence, Riesz space, Unbounded order continuous dual, Unbounded order continuous operator, Unbounded order convergence
• Gazi University Affiliated: Yes

#### Abstract

© TÜBİTAKLet U and V be two Archimedean Riesz spaces. An operator S: (Formula Presented) is said to be unbounded order continuous (uo-continuous), if (Formula Presented) in U implies (Formula Presented). In this paper, we give some properties of the uo-continuous dual (Formula Presented) of U. We show that a nonzero linear functional f on U is uo-continuous if and only if f is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the uo-continuous dual (Formula Presented). In general, by giving an example that the uo-continuous dual (Formula Presented) is not a band in (Formula Presented), we obtain the conditions for the uo-continuous dual of a Banach lattice U to be a band in (Formula Presented). Then, we examine the properties of uo-continuous operators. We show that S is an order continuous operator if and only if S is an unbounded order continuous operator when S is a lattice homomorphism between two Riesz spaces U and V. Finally, we proved that if an order bounded operator S: U → V between Archimedean Riesz space U and atomic Dedekind complete Riesz space V is uo-continuous, then |S| is uo-continuous.