{
  "abstract": "For every $1<p\\neq2<\\infty$, we exhibit an explicit Schur multiplier on $S_p$ whose operator norm is strictly smaller than its completely bounded norm. More precisely, for each such $p$, we construct a finitely supported Schur symbol $m_p$ such that \\[ \\|M_{m_p}\\|_{p\\to p} < \\|M_{m_p}\\|_{\\mathrm{cb},p}. \\] This answers the question raised by Lafforgue and de la Salle in 2011 after their Conjecture~1.8 and gives an affirmative answer to Statement~2 in Section~5 of Caspers and Wildschut (2019). In particular, it disproves Statement~3 of Caspers and Wildschut (2019) throughout the same range of exponents.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20933",
  "author_total": 3,
  "authors": [
    {
      "name": "J. Huang"
    },
    {
      "name": "F. Sukochev"
    },
    {
      "name": "A. Tomskova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zr7d9shs3t2c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20933",
  "fulltext_url": null,
  "id": "1zr7d9shs3t2c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20933",
  "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",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7204106708",
  "pdf_url": "https://arxiv.org/pdf/2608.20933",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zr7d9shs3t2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.20933",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20933"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Schur Multipliers with Unequal Operator and Completely Bounded Norms on $S_p$, $1<p\\ne 2<\\infty $",
  "title_text": "Schur Multipliers with Unequal Operator and Completely Bounded Norms on S_p, $1<p\\ne 2<\\infty $",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1zr7d9shs3t2c",
  "venue": "arXiv",
  "versions": []
}