This is an announcement for the paper “Unbounded absolute weak convergence in Banach lattices” by Omid Zabetihttp://arxiv.org/find/math/1/au:+Zabeti_O/0/1/0/all/0/1.
Abstract: The concepts of unbounded norm convergent nets and unbounded order convergent ones are considered and investigated in several recent papers by Gao, Deng, and et al. In this note, taking idea from these notions, we consider the concept of an unbounded absolute weak convergent (uaw) net in a Banach lattice. A net $(x_\alpha)$ in a Banach lattice E is said to be uaw-convergent to $x\in E$ if for each $u\in E_+$, the net $(|x_\alpha – x|\wedge u)$ converges to zero weakly. We investigate some properties of uaw-convergence and its relationship to other types of unbounded convergent nets. In particular, we characterize order continuous Banach lattices and reflexive Banach lattices in term of uaw-convergence.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1608.02151