{
  "abstract": "Let $LS(\\mathcal{M})$ be the algebra of locally measurable operators affiliated with a von Neumann algebra $\\mathcal{M}$, equipped with an $F$-norm defined via a dimension function and a probability measure. We prove that every bijective linear isometry between $LS(\\mathcal{M})$ admits a canonical representation of the form $Φ(x)=wJ(x)$, where $w$ is a unitary element and $J$ is a Jordan $^*$-isomorphism, which extends classical results such as the Banach--Stone theorem and Kadison's theorem. Under several structural assumptions on the underlying von Neumann algebras (including all type $\\mathrm{II}_\\infty$ and type $\\mathrm{III}$ algebras, and all factors, and algebras with atomless centers), we prove the one-to-one correspondence between the $F$-norm and the pair $(μ, D)$ of a probability measure and a dimension function, which fails for algebras with atomic centers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28710",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinghao Huang"
    },
    {
      "name": "Karimbergen Kudaybergenov"
    },
    {
      "name": "Bing Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/667rc88jhtcyn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28710",
  "fulltext_url": null,
  "id": "667rc88jhtcyn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28710",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7204940320",
  "pdf_url": "https://arxiv.org/pdf/2608.28710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/667rc88jhtcyn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isometries on algebras of locally measurable operators",
  "title_text": "Isometries on algebras of locally measurable operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/667rc88jhtcyn",
  "venue": "arXiv",
  "versions": []
}