{
  "abstract": "Let $T\\colon F\\to E$ be a bounded operator between Banach spaces and let $\\overline T\\colon FBL^{(p)}[F]\\to FBL^{(p)}[E]$ be the lattice homomorphism induced by $T$ between the corresponding free $p$-convex Banach lattices generated by $F$ and $E$. We show that $\\overline T$ is order continuous if and only if it is either zero or a lattice isomorphic embedding. For $p=\\infty$, this holds precisely when $T$ is zero or an isomorphic embedding, while for $1\\leq p<\\infty$, apart from the zero operator, $T$ must be an embedding and the pair $(T(F),E)$ must have the operator-extension property POE-$p$. In addition, we study when $FBL^{(p)}[E]$ is order dense or majorizing in $FBL^{(q)}[E]$ for $p<q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00451",
  "author_total": 2,
  "authors": [
    {
      "name": "Raúl E. Pariente-Martín"
    },
    {
      "name": "Pedro Tradacete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a1q6yzps51nx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00451",
  "fulltext_url": null,
  "id": "8a1q6yzps51nx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00451",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a1q6yzps51nx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Order continuity of induced homomorphisms between free Banach lattices",
  "title_text": "Order continuity of induced homomorphisms between free Banach lattices",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8a1q6yzps51nx",
  "venue": "arXiv",
  "versions": []
}