{
  "abstract": "We show that a two-dimensional complex subspace of $\\ell_\\infty^3$ carries a unique operator space structure if and only if it is isometric to $\\ell_\\infty^2$; the ``if'' half is the Andô's theorem. For each of the remaining spaces we exhibit an explicit non-normal $Y \\in \\mathcal{M}_2$, with $(I,Y)$ an extreme point of the associated matrix ball, for which the induced linear map is contractive but not completely contractive. Since every two-dimensional subspace of $\\ell_\\infty^3$ has the $2$-summing property, the $2$-summing property does not imply uniqueness of the operator space structure for two dimensional complex Banach spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26738",
  "author_total": 4,
  "authors": [
    {
      "name": "Rajeev Gupta"
    },
    {
      "name": "Arpita Mal"
    },
    {
      "name": "Gadadhar Misra"
    },
    {
      "name": "Samya Kumar Ray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avfra70gdkcbt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26738",
  "fulltext_url": null,
  "id": "avfra70gdkcbt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26738",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223067973",
  "pdf_url": "https://arxiv.org/pdf/2610.26738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avfra70gdkcbt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26738"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A two-dimensional subspace of $\\ell_\\infty^3$ has a unique operator space structure if and only if it is isometric to $\\ell_\\infty^2$",
  "title_text": "A two-dimensional subspace of ℓ_∞^3 has a unique operator space structure if and only if it is isometric to ℓ_∞^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/avfra70gdkcbt",
  "venue": "arXiv",
  "versions": []
}