A review on unbounded absolute weak convergence in Banach lattices

A net $(x_{\alpha})$ in a Banach lattice $E$ is said to be unbounded absolutely weakly convergent ($uaw$-convergent, in brief) to $x\in E$ if for each $u\in E_{+}$, the net $(|x_{\alpha}-x|\wedge u)$ converges to zero weakly. In this paper, We consider some properties of $uaw$-convergence.