{
  "abstract": "We investigate max-phase isometries on Schatten quasi-classes in the range $0<p<1$. Motivated by the rigidity theory for smooth normed spaces [\\emph{Results Math.} \\textbf{80} (2025), Article 126], we establish its operator-theoretic counterpart in the quasi-Banach setting. We prove that every surjective max-phase isometry on a finite-dimensional Schatten class is a standard real-linear Schatten isometry multiplied by an even sign-valued function, without any continuity assumption. This extends the scope of the classical Schatten isometry classification [\\emph{Proc. Edinburgh Math. Soc.} \\textbf{37} (1994), 239--242] to nonlinear mappings preserving only unsigned two-point metric data. Our approach combines support orthogonality, a symmetrized rank-one spectral formula, and a max-profile uniqueness principle. For arbitrary Hilbert spaces, we obtain the corresponding classification on finite-rank operators, while continuity yields the full-space result. We also establish preservation of rank, singular values, and two-sided support orthogonality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13271",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenwen Zhang"
    },
    {
      "name": "Qi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/288nbar2kxqq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13271",
  "fulltext_url": null,
  "id": "288nbar2kxqq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13271",
  "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": "W7221559875",
  "pdf_url": "https://arxiv.org/pdf/2610.13271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/288nbar2kxqq6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Surjective Max-Phase Isometries of Schatten p-Classes (0<p<1)",
  "title_text": "On Surjective Max-Phase Isometries of Schatten p-Classes (0<p<1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/288nbar2kxqq6",
  "venue": "arXiv",
  "versions": []
}