{
  "abstract": "We study weak almost periodicity and left uniform continuity for Hopf-von Neumann algebras and locally compact quantum groups. For a Hopf-von Neumann algebra $(M,Γ)$, we introduce the space ${\\rm WAP}_{{\\rm Bessel},π_u}(M_*)$ through norm convergence conditions on rows and columns of slices associated with Bessel families in the universal representation. We prove that this space is the largest $C^*$-subalgebra of ${\\rm WAP}(M_*)$ when separately continuous lift of the co-multiplication is multiplicative, and that the two spaces coincide when $M$ is commutative. Furthermore, the algebra $\\{x\\in C_b(\\mathbb{G}): Γ(x)\\in M(C_0(\\mathbb{G})\\otimes C_b(\\mathbb{G}))\\}$ is characterized as the greatest left introverted $C^*$-subalgebra of ${\\rm LUC}(L^1(\\mathbb{G}))$ satisfying a left Bessel condition on $L^2(\\mathbb{G})$. We also show that ${\\rm LUC}(L^1(\\mathbb{G}))$ is a $C^*$-algebra whenever the center of $C_0(\\mathbb{G})$ contains an element on which the bounded counit is non-zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07168",
  "author_total": 3,
  "authors": [
    {
      "name": "Ramin Faal"
    },
    {
      "name": "Amin Allah Khosravi"
    },
    {
      "name": "Hamid Reza Ebrahimi Vishki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0g2fd9x12rc37.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07168",
  "fulltext_url": null,
  "id": "0g2fd9x12rc37",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07168",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07168",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0g2fd9x12rc37.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07168",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07168"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Noncommutative weak almost periodicity and left uniform continuity over locally compact quantum groups",
  "title_text": "Noncommutative weak almost periodicity and left uniform continuity over locally compact quantum groups",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/0g2fd9x12rc37",
  "venue": "arXiv",
  "versions": []
}