Unbounded absolute weak convergence in Banach lattices
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.
KeywordsBanach lattice Unbounded absolute weak convergence Unbounded absolute weak topology Order continuous Banach lattice Reflexive Banach lattice
Mathematics Subject ClassificationPrimary 46B42 54A20 Secondary 46B40
This note would not have existed without inspiring and worthwhile suggestions of V. G. Troitsky, my friend and my colleague. Thanks is also due to Niushan Gao and Foivos Xanthos for useful remarks. I would like to have a deep gratitude toward the referee for invaluable comments which improved the paper in the present form.