{
  "abstract": "Let $T$ be a bounded self-adjoint operator on a separable infinite-dimensional right quaternionic Hilbert space, and let $\\sigdS(T)$ be the set of right eigenvalues of finite type. We prove that Weyl's theorem holds for $T$: $$\\sigeS(T)=\\sigS(T)\\setminus\\sigdS(T),$$ which completes the inclusion obtained in the general case. The proof proceeds through a single three-way criterion: a point of $\\sigS(T)$ lies outside $\\sigeS(T)$, and equally lies in $\\sigdS(T)$, exactly when it is isolated with a spectral atom of finite rank. The natural route through Riesz projections is not available as it stands, because a Riesz projection need not be orthogonal; we show that for a self-adjoint operator it in fact is, the Riesz projection of an isolated spectral part coinciding with the corresponding spectral projection, so that the algebraic and geometric multiplicities agree. A $2\\times2$ quaternionic matrix shows that this last identity fails without self-adjointness, and a normal operator with genuinely spherical $S$-spectrum shows what has to change in the normal case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23682",
  "author_total": 3,
  "authors": [
    {
      "name": "Hatem Baloudi"
    },
    {
      "name": "Mohamed Ali Dbeibia"
    },
    {
      "name": "Kamel Mahfoudhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4w6rfp871qnmq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23682",
  "fulltext_url": null,
  "id": "4w6rfp871qnmq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23682",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214040906",
  "pdf_url": "https://arxiv.org/pdf/2609.23682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4w6rfp871qnmq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weyl's Theorem for Bounded Self-Adjoint Operators",
  "title_text": "Weyl's Theorem for Bounded Self-Adjoint Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4w6rfp871qnmq",
  "venue": "arXiv",
  "versions": []
}