{
  "abstract": "Let \\(M\\) be a Hopf--von Neumann algebra with predual \\(M_*\\). Using minimal weak*-closed left ideals, we obtain an idempotent state \\(φ\\in\\operatorname{WAP}(M_*)^*\\) satisfying \\(φ\\star ω\\starφ=φ\\) for every state \\(ω\\) on \\(\\operatorname{WAP}(M_*)\\). This state determines the largest closed introverted subspace \\(X_φ\\subseteq\\operatorname{WAP}(M_*)\\) containing the identity and admitting a two-sided invariant mean. We also characterize the existence of a unique two-sided invariant mean on introverted operator systems in \\(\\operatorname{WAP}(M_*)\\) by a symmetry condition on their left and right state orbits. The criterion recovers the classical results for locally compact groups and their Fourier algebras, and gives a unified treatment of cocommutative Hopf--von Neumann algebras, compact quantum groups, unital \\(C^*\\)-Eberlein algebras, and \\(\\operatorname{WAP}(M(G))\\) for every locally compact group \\(G\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00431",
  "author_total": 3,
  "authors": [
    {
      "name": "Ramin Faal"
    },
    {
      "name": "Hamid Reza Ebrahimi Vishki"
    },
    {
      "name": "Amin Allah Khosravi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4271w7bbag70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00431",
  "fulltext_url": null,
  "id": "a4271w7bbag70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00431",
  "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/2611.00431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4271w7bbag70.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Invariant mean on weakly almost periodic functionals over a Hopf-von Neumann algebra",
  "title_text": "Invariant mean on weakly almost periodic functionals over a Hopf-von Neumann algebra",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/a4271w7bbag70",
  "venue": "arXiv",
  "versions": []
}