Positivity

, Volume 22, Issue 2, pp 501–505 | Cite as

Unbounded absolute weak convergence in Banach lattices

Article

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.

Keywords

Banach lattice Unbounded absolute weak convergence Unbounded absolute weak topology Order continuous Banach lattice Reflexive Banach lattice 

Mathematics Subject Classification

Primary 46B42 54A20 Secondary 46B40 

Notes

Acknowledgements

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.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of MathematicsUniversity of Sistan and BaluchestanZahedanIran

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