Continuous functionals for unbounded convergence in Banach lattices
Functional Analysis
2021-04-01 v2
Abstract
Recently, the different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous functionals with respect to unbounded convergences. We first characterize the continuity of linear functionals for these convergences. Then we define the corresponding unbounded dual spaces and get their exact form. Based on these results, we discuss order continuity and reflexivity of Banach lattices. Some related results are obtained as well.
Cite
@article{arxiv.2003.06610,
title = {Continuous functionals for unbounded convergence in Banach lattices},
author = {Zhangjun Wang and Zili Chen and Jinxi Chen},
journal= {arXiv preprint arXiv:2003.06610},
year = {2021}
}
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9 pages