Bibounded uo-convergence and b-property in vector lattices

Abstract

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 $⟨X,X^{\sim }⟩$, $X$ has $b$-property if and only if the order convergence in $X$ agrees with the order convergence in $X^{\sim \sim }$.