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Unbounded absolute weak convergence in Banach lattices

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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.

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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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  1. Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

    Omid Zabeti

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  1. Omid Zabeti
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Correspondence to Omid Zabeti.

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Zabeti, O. Unbounded absolute weak convergence in Banach lattices. Positivity 22, 501–505 (2018). https://doi.org/10.1007/s11117-017-0524-7

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  • DOI: https://doi.org/10.1007/s11117-017-0524-7

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