{
  "abstract": "Let $E$ be a Hilbert C*-module and $\\mathcal{L}(E)$ the C*-algebra of all bounded adjointable operators on $E$. An operator $T \\in \\mathcal{L}(E)$ is a Kasparov cycle if $T^*T - 1$ and $TT^*-1$ are compact operators on $E$. If $\\mathcal{L}(E)\\rightarrow \\mathcal{L}(E)$ is a prime C*-algebra, and $φ:\\mathcal{L}(E)\\rightarrow \\mathcal{L}(E)$ is a linear map which is unital and surjective up to compact operators, and preserves Kasparov cycles in both directions, then the induced map $ψ:\\mathcal{L}(E)/\\mathcal{K}(E) \\rightarrow \\mathcal{L}(E)/\\mathcal{K}(E)$ is either a $*$-automorphism or a $*$-anti-automorphism. Our work extends the main result of [J. Math. Anal. Appl. 354 (2009), 625-629] to the set of Kasparov cycles, showing that the assumption ``$\\mathcal{L}(E)/\\mathcal{K}(E)$ has real rank zero'' is redundant in our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18619",
  "author_total": 1,
  "authors": [
    {
      "name": "Kamran Sharifi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32qsygc7hk7yw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18619",
  "fulltext_url": null,
  "id": "32qsygc7hk7yw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18619",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32qsygc7hk7yw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18619"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Linear maps preserving Kasparov cycles and the characterization of induced automorphisms",
  "title_text": "Linear maps preserving Kasparov cycles and the characterization of induced automorphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/32qsygc7hk7yw",
  "venue": "arXiv",
  "versions": []
}