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 \(\langle X,X^{\sim }\rangle \), X has b-property if and only if the order convergence in X agrees with the order convergence in \(X^{\sim \sim }\).