Some results on unbounded absolute weak convergence

Abstract

In this paper, we establish the stability of uaw-convergence under passing from sublattices. The various implications of this fact are presented through the paper. In particular, we show that if \((x_{\alpha })\) is an increasing net in a Banach lattice E and \(x_{\alpha }\overset{uaw}{\longrightarrow }0\) in E then \(x_{\alpha }\overset{un}{\longrightarrow }0\) in \(E^{''}\). Furthermore, we deduce some results concerning uaw-completeness. Additionally, we present a new characterizations of KB-spaces (resp. reflexive Banach lattices), using the concepts of uaw-convergence and un-convergence.