{
  "abstract": "We develop an analytic framework for the explicit construction of Kasparov products on uncountably generated Hilbert modules over non-separable C$^*$-algebras by extending the classical Kasparov bimodule picture. In particular, this yields a well-defined functor from the category of general C$^*$-algebras whose restriction to separable C$^*$-algebras coincides with classical KK-theory and which satisfies several properties expected of non-separable KK-theory. A key idea of the extension is to replace a single Fredholm operator on a Kasparov bimodule with a net and to encode the directed system of separable C$^*$-subalgebras. We also introduce the notion of freely complementable Hilbert modules and develop cropping techniques to extend Kasparov's technical theorem beyond the countably generated setting. It naturally gives rise to a sufficiently broad class of C$^*$-algebras that provides a non-commutative analogue of paracompactness and includes all $σ$-unital algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40351",
  "author_total": 1,
  "authors": [
    {
      "name": "Ikhan Choi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84ycrk4khgsdz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40351",
  "fulltext_url": null,
  "id": "84ycrk4khgsdz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40351",
  "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.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84ycrk4khgsdz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Analytic Kasparov product for non-separable C$^*$-algebras",
  "title_text": "Analytic Kasparov product for non-separable C^*-algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/84ycrk4khgsdz",
  "venue": "arXiv",
  "versions": []
}