{
  "abstract": "We characterize extreme points of the (positive) unit balls of Marcinkiewicz spaces with respect to their natural quasi-norms. Having these results at hand, we show that every positive surjective isometry on a noncommutative Marcinkiewicz space is of elementary form. In particular, a linear mapping on a noncommutative Marcinkiewicz space over an atomic von Neumann algebra with all atoms having the same trace is a positive surjective isometry if and only if it is the restriction of a Jordan $*$-isomorphism which preserves the singular value functions. We also study (not necessarily positive) surjective isometries on weak $L_p$-spaces affiliated a $σ$-finite non-atomic von Neumann algebra for $1<p<\\infty$, Marcinkiewicz sequence spaces, and weak $\\ell_p$ operator ideals, $p>0$, as well as one-parameter groups of isometries on the latter two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01043",
  "author_total": 4,
  "authors": [
    {
      "name": "Kai Fang"
    },
    {
      "name": "Yi Gao"
    },
    {
      "name": "Jinghao Huang"
    },
    {
      "name": "Fedor Sukochev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edxz3nrtv62xb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01043",
  "fulltext_url": null,
  "id": "edxz3nrtv62xb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01043",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222115900",
  "pdf_url": "https://arxiv.org/pdf/2610.01043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edxz3nrtv62xb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.01043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extreme points of the unit balls and isometries of noncommutative quasi-Banach Marcinkiewicz spaces",
  "title_text": "Extreme points of the unit balls and isometries of noncommutative quasi-Banach Marcinkiewicz spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/edxz3nrtv62xb",
  "venue": "arXiv",
  "versions": []
}