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PreprintarXiv licencearXiv

Order closure, order adherence and Fatou norms

  • A. Avilés
  • M. A. Taylor
  • P. Tradacete
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Abstract

We record two results in the theory of vector and Banach lattices related to order adherence. First, we give a negative answer to Gao and Leung's question on whether the uo-adherence of sublattices must be order closed. Second, we present a self-contained counterexample showing that a Banach lattice with a weakly Fatou norm need not admit any equivalent lattice norm with the Fatou property.

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Cite

BibTeXRIS
BibTeX
@misc{aviles2026order,
  title = {{Order closure, order adherence and Fatou norms}},
  author = {A. Avilés and M. A. Taylor and P. Tradacete},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06689},
  eprint = {2609.06689},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06689},
}
RIS
TY  - UNPB
TI  - Order closure, order adherence and Fatou norms
AU  - A. Avilés
AU  - M. A. Taylor
AU  - P. Tradacete
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06689
UR  - https://arxiv.org/abs/2609.06689
AB  - We record two results in the theory of vector and Banach lattices related to order adherence. First, we give a negative answer to Gao and Leung's question on whether the uo-adherence of sublattices must be order closed. Second, we present a self-contained counterexample showing that a Banach lattice with a weakly Fatou norm need not admit any equivalent lattice norm with the Fatou property.
ER  -