Bibounded uo-convergence and b-property in vector lattices

Alpay S., EMELYANOV E., Gorokhova S.

Positivity, cilt.25, sa.5, ss.1677-1684, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s11117-021-00840-7
  • Dergi Adı: Positivity
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1677-1684
  • Anahtar Kelimeler: Vector lattice, Order dual, Regular Riesz dual system, b-property, Unbounded order convergence, Banach lattice, UNBOUNDED ORDER CONVERGENCE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.