Unbounded absolute weak convergence in Banach lattices

TL;DR

This paper explores unbounded absolute weak convergence in Banach lattices, characterizing key lattice properties like order continuity and reflexivity through this convergence type.

Contribution

It introduces and analyzes the unbounded absolute weak convergence, linking it to fundamental properties of Banach lattices such as order continuity and reflexivity.

Findings

Characterizes order continuous Banach lattices via unbounded absolute weak convergence.

Provides criteria for reflexive Banach lattices using this convergence.

Establishes relationships between unbounded weak convergence and other convergence modes.

Abstract

Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its relationship with other convergences. In particular, we characterize order continuous Banach lattices and reflexive Banach lattices in terms of this convergence.