{
  "abstract": "The Ulam--Kaplansky problem up to similarity in operator algebras asks whether $A\\oplus A\\sim B\\oplus B$ implies $A\\sim B$. We construct block-diagonal compact operators for which this implication fails. For von Neumann algebras with separable predual, we prove that this cancellation property is equivalent to subhomogeneity. Moreover, we obtain a cancellation law for finite ampliations in unital Banach algebras when the commutant of one element is finite dimensional modulo its Jacobson radical.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20593",
  "author_total": 4,
  "authors": [
    {
      "name": "Chunlan Jiang"
    },
    {
      "name": "Minghui Ma"
    },
    {
      "name": "Rui Shi"
    },
    {
      "name": "Yuanhang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sf3kkkwvby43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20593",
  "fulltext_url": null,
  "id": "9sf3kkkwvby43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20593",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7170391066",
  "pdf_url": "https://arxiv.org/pdf/2607.20593",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sf3kkkwvby43.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2607.20593",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20593"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Ulam--Kaplansky problem in operator algebras",
  "title_text": "The Ulam--Kaplansky problem in operator algebras",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/9sf3kkkwvby43",
  "venue": "arXiv",
  "versions": []
}