{
  "abstract": "Let $A$ be a bounded operator on a separable right quaternionic Hilbert space and let $\\CA$ be the set of compact operators commuting with $A$. We establish the formula \\[ \\sigb(A)=\\bigcap_{K\\in\\CA} \\sS(A+K), \\] a quaternionic analogue of the classical characterization of the complex Browder spectrum. The proof rests on a factorization lemma (Lemma~\\ref{lem:fact}), a consequence of the Riesz--Schauder theorem and an ascent/descent argument, and on the characterization $\\sigb(A)=\\sS(A)\\setminus\\sd(A)$ in terms of S-eigenvalues of finite type, due to Arzini and Jaatit \\cite{AJ26}, for which we give here an independent proof (Lemma~\\ref{lem:A}). We also record two consequences of independent interest: the intersection defining $\\sigb(A)$ may be restricted, without loss, to \\emph{finite-rank} operators commuting with $A$ (Corollary~\\ref{cor:finite}); and, by a separate argument resting on the ascent/descent stability results of \\cite{KD24}, the stronger pointwise statement $\\sigb(A+K)=\\sigb(A)$ holds for a fixed $K\\in\\CA$ and arbitrary $A\\in\\B(\\V)$ (Theorem~\\ref{thm:pointwise}), known in the complex case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10616",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Ali Dbeibia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3by25t9d0nvvr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10616",
  "fulltext_url": null,
  "id": "3by25t9d0nvvr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10616",
  "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.FA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7212281172",
  "pdf_url": "https://arxiv.org/pdf/2609.10616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3by25t9d0nvvr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A note on the Browder S-spectrum of a bounded quaternionic operator",
  "title_text": "A note on the Browder S-spectrum of a bounded quaternionic operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/3by25t9d0nvvr",
  "venue": "arXiv",
  "versions": []
}