{
  "abstract": "We establish an operator-valued Fejer-Riesz factorization theorem for the algebraic free product A of C[F], the group algebra on the free group F on finitely many generators, with finitely many finite dimensional C-star algebras. With respect to a natural reduced-word length, called extent, we show that every linear combination F of elements of A with coefficients from the algebra of operators on a Hilbert space of extent at most 2d that is positive under all finite-dimensional unital *-representations of A admits a factorization F=B^*B with B of extent at most d. This sharp half-extent bound holds without strict positivity. The proof combines a new finite-dimensional realization theorem for positive truncated kernels with operator-system methods. We also establish factorization results for tensor products with group algebras of arbitrary discrete groups under strict positivity in the maximal C-star-tensor product; for amenable groups, strict positivity in the minimal tensor product suffices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08554",
  "author_total": 4,
  "authors": [
    {
      "name": "Abhay Jindal"
    },
    {
      "name": "Igor Klep"
    },
    {
      "name": "Jacob Levenson"
    },
    {
      "name": "Scott McCullough"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/848040b6wc1nd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08554",
  "fulltext_url": null,
  "id": "848040b6wc1nd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08554",
  "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/2611.08554",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/848040b6wc1nd.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08554",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08554"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fejer-Riesz factorization for free products",
  "title_text": "Fejer-Riesz factorization for free products",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/848040b6wc1nd",
  "venue": "arXiv",
  "versions": []
}