{
  "abstract": "In this paper unbounded representations of quasi *-algebras on an indefinite inner product space are introduced and studied. After introducing the partial *-algebra of unbounded closable operators sharing a common dense domain in a Krein space, the appropriate notion of *-representation in this setting is developed, and a GNS-type construction for quasi *-algebras based on $α$-positive sesquilinear forms is established. Furthermore, the notion of abstract conditional expectation is generalized to quasi *-algebras and how \\emph{admissible} abstract conditional expectations $P$ give rise to representable $P$-forms is shown. The relation between $α$-positive forms and $P$-forms is also clarified. Several examples are provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08329",
  "author_total": 1,
  "authors": [
    {
      "name": "Giorgia Bellomonte"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66h95qt03asyt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08329",
  "fulltext_url": null,
  "id": "66h95qt03asyt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08329",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66h95qt03asyt.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08329"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "GNS-like representations of a quasi *-algebra in Krein spaces",
  "title_text": "GNS-like representations of a quasi *-algebra in Krein spaces",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/66h95qt03asyt",
  "venue": "arXiv",
  "versions": []
}