{
  "abstract": "We determine the cotangent operator space structure at the origin of the tetrablock (denoted by $\\mathbb E$). In particular we prove that $\\operatorname{COT}_0(\\overline{\\mathbb E}) =\\operatorname{MIN}(\\ell_1^2\\oplus_\\infty\\mathbb C)$ completely isometrically. This shows the existence of commuting tuple of operators having $\\overline{\\mathbb E}$ as a spectral set but not as a complete spectral set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37698",
  "author_total": 2,
  "authors": [
    {
      "name": "Shubhankar Mandal"
    },
    {
      "name": "Samya Kumar Ray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/293eqxw2kb7sj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37698",
  "fulltext_url": null,
  "id": "293eqxw2kb7sj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37698",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214904170",
  "pdf_url": "https://arxiv.org/pdf/2609.37698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/293eqxw2kb7sj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37698"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms",
  "title_text": "Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/293eqxw2kb7sj",
  "venue": "arXiv",
  "versions": []
}