{
  "abstract": "Given an orthogonal decomposition \\(\\widetilde{\\mathfrak{H}} = \\mathfrak{H}[\\dotplus]\\widehat{\\mathfrak{H}}\\) of a Krein space, we study compressions \\({\\mathrm{C}_{\\mathfrak H}}(R)\\) of linear relations \\(R\\) in \\(\\widetilde{\\mathfrak{H}}\\) to \\(\\mathfrak{H}\\). We formulate a sufficient condition that ensures that compression commutes with taking adjoints, that is, the adjoint identity \\({\\mathrm{C}_{\\mathfrak H}}(R^{\\widetilde{*}}) = {\\mathrm{C}_{\\mathfrak H}}(R)^{*}\\) holds. We derive preservation and reflection results for the compression of maximal dissipative, maximal symmetric, and self-adjoint linear relations. For nonnegative linear relations, the adjoint identity also implies that compression commutes with taking the Friedrichs extension. For \\(\\mathfrak{H}\\ne\\{0\\}\\), we characterize finite dimensionality of the exit space \\(\\widehat{\\mathfrak{H}}\\) by universal compression properties. Finally, we give a criterion for the adjoint identity to hold in terms of bounded linear functionals on \\(R\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07299",
  "author_total": 2,
  "authors": [
    {
      "name": "Branko Ćurgus"
    },
    {
      "name": "Aad Dijksma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejxkfehcg6h1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07299",
  "fulltext_url": null,
  "id": "ejxkfehcg6h1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07299",
  "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/2611.07299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejxkfehcg6h1p.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Compressions of Linear Relations in Krein Spaces",
  "title_text": "Compressions of Linear Relations in Krein Spaces",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/ejxkfehcg6h1p",
  "venue": "arXiv",
  "versions": []
}