{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06689",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Avilés"
    },
    {
      "name": "M. A. Taylor"
    },
    {
      "name": "P. Tradacete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xg7eskyxqt38.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06689",
  "fulltext_url": null,
  "id": "6xg7eskyxqt38",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06689",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7212041655",
  "pdf_url": "https://arxiv.org/pdf/2609.06689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xg7eskyxqt38.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Order closure, order adherence and Fatou norms",
  "title_text": "Order closure, order adherence and Fatou norms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6xg7eskyxqt38",
  "venue": "arXiv",
  "versions": []
}