{
  "abstract": "We study the Arens regularity of the Fremlin projective tensor product of Banach lattice algebras. We firrst introduce and investigate L-weakly almost periodic functionals, a class of functionals defind in terms of L-weak compactness of their orbits. We obtain a characterization of these functionals in terms of bounded disjoint sequences and use it to analyze the Fremlin projective tensor product. In particular, we prove that, for nontrivial Banach attice algebras A and B, Arens regularity of A j jB implies Arens regularity of both A and B. The converse, however, fails: we construct two Arens regular Banach lattice algebras whose Fremlin projective tensor product is not Arens regular. We also establish several sufficient conditions for the Arens regularity of A j jB, including conditions involving the positive Schur property and order continuity of the norm on the space of regular operators. Finally, we show that when both factors are Banach f-algebras, their Fremlin projective tensor product is Arens regular.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13734",
  "author_total": 2,
  "authors": [
    {
      "name": "Jamel Jaber"
    },
    {
      "name": "Marwa Troudi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4f3mvbmp4vyt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13734",
  "fulltext_url": null,
  "id": "4f3mvbmp4vyt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13734",
  "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": "W7221560256",
  "pdf_url": "https://arxiv.org/pdf/2610.13734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4f3mvbmp4vyt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13734"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The tensor product of the Fremlin tensor product of Banach lattice algebras",
  "title_text": "The tensor product of the Fremlin tensor product of Banach lattice algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/4f3mvbmp4vyt6",
  "venue": "arXiv",
  "versions": []
}