Bibounded uo-convergence and b-property in vector lattices


Alpay S., EMELYANOV E. , Gorokhova S.

Positivity, vol.25, no.5, pp.1677-1684, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1007/s11117-021-00840-7
  • Title of Journal : Positivity
  • Page Numbers: pp.1677-1684
  • Keywords: Vector lattice, Order dual, Regular Riesz dual system, b-property, Unbounded order convergence, Banach lattice, UNBOUNDED ORDER CONVERGENCE

Abstract

© 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∼ ∼.