{
  "abstract": "Following \\cite{BR} we study hyponormal operators in the strictly larger class $β(H)$ of operators whose restriction to every non-zero reducing subspace is norm attaining. The Weyl-type characterization of positive operators via the essential spectrum used in the absolutely norm attaining case is replaced by a well-ordering condition on the eigenvalues (Theorem~\\ref{thm:positive}). We prove a transfinite, block-diagonal representation $T=\\bigoplus_iλ_iS_i$ (with isometries $S_i$) for the $β(H)$-operators whose $|T|$-eigenspaces are reducing, equivalently the quasinormal operators with $|T|\\inβ(H)$, and we show by examples that hyponormality alone does not give such a decomposition. For normal operators we obtain a complete representation, and for hyponormal $β(H)$-operators we show that normality is equivalent to the spectrum having planar Lebesgue measure zero. An analogous area-zero criterion for normality is proved for hyponormal operators attaining the minimum modulus on every non-zero reducing subspace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13490",
  "author_total": 3,
  "authors": [
    {
      "name": "Ramesh Golla"
    },
    {
      "name": "Hiroyuki Osaka"
    },
    {
      "name": "Shanola S. Sequeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dga9ep4wpkda0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13490",
  "fulltext_url": null,
  "id": "dga9ep4wpkda0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13490",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7221516276",
  "pdf_url": "https://arxiv.org/pdf/2610.13490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dga9ep4wpkda0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quasinormal and hyponormal operators in the $β(H)$-class",
  "title_text": "Quasinormal and hyponormal operators in the β(H)-class",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/dga9ep4wpkda0",
  "venue": "arXiv",
  "versions": []
}