On unbounded order continuous operators
Yıl: 2022 Cilt: 46 Sayı: 8 Sayfa Aralığı: 3391 - 3399 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3339 İndeks Tarihi: 02-01-2023
On unbounded order continuous operators
Öz: 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.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA | TURAN B, Altın B, Gürkök H (2022). On unbounded order continuous operators. , 3391 - 3399. 10.55730/1300-0098.3339 |
Chicago | TURAN BAHRİ,Altın Birol,Gürkök Hüma On unbounded order continuous operators. (2022): 3391 - 3399. 10.55730/1300-0098.3339 |
MLA | TURAN BAHRİ,Altın Birol,Gürkök Hüma On unbounded order continuous operators. , 2022, ss.3391 - 3399. 10.55730/1300-0098.3339 |
AMA | TURAN B,Altın B,Gürkök H On unbounded order continuous operators. . 2022; 3391 - 3399. 10.55730/1300-0098.3339 |
Vancouver | TURAN B,Altın B,Gürkök H On unbounded order continuous operators. . 2022; 3391 - 3399. 10.55730/1300-0098.3339 |
IEEE | TURAN B,Altın B,Gürkök H "On unbounded order continuous operators." , ss.3391 - 3399, 2022. 10.55730/1300-0098.3339 |
ISNAD | TURAN, BAHRİ vd. "On unbounded order continuous operators". (2022), 3391-3399. https://doi.org/10.55730/1300-0098.3339 |
APA | TURAN B, Altın B, Gürkök H (2022). On unbounded order continuous operators. Turkish Journal of Mathematics, 46(8), 3391 - 3399. 10.55730/1300-0098.3339 |
Chicago | TURAN BAHRİ,Altın Birol,Gürkök Hüma On unbounded order continuous operators. Turkish Journal of Mathematics 46, no.8 (2022): 3391 - 3399. 10.55730/1300-0098.3339 |
MLA | TURAN BAHRİ,Altın Birol,Gürkök Hüma On unbounded order continuous operators. Turkish Journal of Mathematics, vol.46, no.8, 2022, ss.3391 - 3399. 10.55730/1300-0098.3339 |
AMA | TURAN B,Altın B,Gürkök H On unbounded order continuous operators. Turkish Journal of Mathematics. 2022; 46(8): 3391 - 3399. 10.55730/1300-0098.3339 |
Vancouver | TURAN B,Altın B,Gürkök H On unbounded order continuous operators. Turkish Journal of Mathematics. 2022; 46(8): 3391 - 3399. 10.55730/1300-0098.3339 |
IEEE | TURAN B,Altın B,Gürkök H "On unbounded order continuous operators." Turkish Journal of Mathematics, 46, ss.3391 - 3399, 2022. 10.55730/1300-0098.3339 |
ISNAD | TURAN, BAHRİ vd. "On unbounded order continuous operators". Turkish Journal of Mathematics 46/8 (2022), 3391-3399. https://doi.org/10.55730/1300-0098.3339 |