On unbounded order continuous operators 2

TURAN B., Gürkök H.

Positivity, cilt.28, sa.1, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11117-023-01021-4
  • Dergi Adı: Positivity
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Order convergence, Riesz space, Unbounded order continuous operator, Unbounded order convergence
  • Gazi Üniversitesi Adresli: Evet

Özet

Let E and F be two Archimedean Riesz spaces. An operator T: E→ F is said to be unbounded order continuous (uo-continuous), if uα→ uo0 in E implies Tuα→ uo0 in F. In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this, we obtain that the space Luo(E, F) of order bounded unbounded order continuous operators is an ideal in Lb(E, F) for Dedekind complete Riesz space F. In general, by giving an example that the space Luo(E, F) of order bounded unbounded order continuous operators is not a band in Lb(E, F) , we obtain the conditions on E or F for the space Luo(E, F) to be a band in Lb(E, F) . Then, we give the extension theorem for uo-continuous operators similar to Veksler’s theorem for order continuous operators.