Some results on unbounded absolute weak convergence

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 \((x_{\alpha })\) $(x_{\alpha })$ is an increasing net in a Banach lattice E and \(x_{\alpha }\overset{uaw}{\longrightarrow }0\) $x_{\alpha }\stackrel{\mathit{uaw}}{⟶}0$ in E then \(x_{\alpha }\overset{un}{\longrightarrow }0\) $x_{\alpha }\stackrel{\mathit{un}}{⟶}0$ in \(E^{''}\) $E^{{}^{\prime \prime }}$ . 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.