{
  "abstract": "It is known that the free $p$-convex Banach lattice on a Banach space $X$ can be represented as a space of functions on the unit ball of $X^*$. In this way, it gives rise to certain related (larger) lattices. To investigate such lattices, we introduce a new tool, related to operators into $X$. This tool is then used to (i) determine whether the lattices in question possess, or fail, properties involving upper bounds of upward directed sets -- namely, the Fatou property, and the related property of monotonic boundedness; (ii) investigate the regularity of embeddings between spaces in question. We find connections between the Fatou-like properties of ${\\textrm{FBL}}^{(p)}[X]$ and the Radon-Nikodym property of $X$. In addition, we give an example of $X \\subset Y$ such that ${\\textrm{FBL}}^{(p)}[X]$ is not a regular sublattice of ${\\textrm{FBL}}^{(p)}[Y]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11928",
  "author_total": 2,
  "authors": [
    {
      "name": "Anastasiia Ianina"
    },
    {
      "name": "Timur Oikhberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmdgamfmck5d6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11928",
  "fulltext_url": null,
  "id": "cmdgamfmck5d6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11928",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7212322430",
  "pdf_url": "https://arxiv.org/pdf/2609.11928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmdgamfmck5d6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Upper bound properties of free and related Banach lattices via operators",
  "title_text": "Upper bound properties of free and related Banach lattices via operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cmdgamfmck5d6",
  "venue": "arXiv",
  "versions": []
}