Unbounded convergence in Banach lattices and applications

Zhangjun Wang; Zili Chen; Jinxi Chen

Unbounded convergence in Banach lattices and applications

Functional Analysis 2021-04-06 v9

Authors: Zhangjun Wang , Zili Chen , Jinxi Chen

Abstract

Several recent papers investigated unbounded convergences in Banach lattices. Combine all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly compact operators and M-weakly compact operators on Banach lattices. Some related results are obtained as well.

Keywords

banach lattices unbounded convergence l-weakly compact sets l-weakly compact operators m-weakly compact operators unbounded order convergence

Cite

@article{arxiv.1903.02168,
  title  = {Unbounded convergence in Banach lattices and applications},
  author = {Zhangjun Wang and Zili Chen and Jinxi Chen},
  journal= {arXiv preprint arXiv:1903.02168},
  year   = {2021}
}

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9 pages

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