TY  - JOUR
TI  - On unbounded order continuous operators
AB  - Let U and V be two Archimedean Riesz spaces. An operator S : U → V is said to be unbounded order continuous ( uo -continuous), if rα uo→ 0 in U implies Srα uo→ 0 in V . In this paper, we give some properties of the uo -continuous dual U ∼ uo 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 U ∼ uo. In general, by giving an example that the uo -continuous dual U ∼ uo is not a band in U ∼ , we obtain the conditions for the uo -continuous dual of a Banach lattice U to be a band in U ∼ . 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.
AU  - Gürkök, Hüma
AU  - Altın, Birol
AU  - TURAN, BAHRİ
DO  - 10.55730/1300-0098.3339
PY  - 2022
JO  - Turkish Journal of Mathematics
VL  - 46
IS  - 8
SN  - 1300-0098
SP  - 3391
EP  - 3399
DB  - TRDizin
UR  - http://search/yayin/detay/1147303
ER  -