{
  "abstract": "In this article, we introduce and study the class $\\mathcal{M}_r(H)$ of minimum attaining operators on a separable Hilbert space $H$ whose restrictions to every nonzero reducing subspace are minimum attaining. This class lies between the classes of absolutely minimum attaining operators and minimum attaining operators. We establish a spectral characterization of positive operators in $\\mathcal{M}_r(H)$: a positive operator $T$ belongs to $\\mathcal{M}_r(H)$ if and only if $T=\\sum_{λ\\inΛ}λP_λ$, where $Λ\\subseteq[0,\\|T\\|]$ is a countable well-ordered set, $(P_λ)_{λ\\inΛ}$ is a family of mutually orthogonal nonzero projections, and $\\sum_{λ\\inΛ}P_λ=I$ in the strong operator topology. We also establish a connection between $\\mathcal{M}_r(H)$ and the class of operators attaining their norm on every nonzero reducing subspace. Further, we obtain stability results under suitable finite-rank and compact perturbations, and prove that $\\mathcal{M}_r(H)$ is norm dense in $\\mathcal{B}(H)$. We also establish the norm density of operators in this class having a nontrivial invariant half-space. Finally, we characterize normal operators in $\\mathcal{M}_r(H)$, obtain a corresponding characterization for multiplication operators on $L^2(\\mathbb{T})$, and characterize the condition $\\mathcal{R}_T=\\mathcal{R}_{|T|}$ in terms of the von Neumann algebra generated by $|T|$, showing that this condition forces $T$ to be normal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19286",
  "author_total": 2,
  "authors": [
    {
      "name": "Nag Puspendu"
    },
    {
      "name": "Golla Ramesh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70xx4yz7zs95a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19286",
  "fulltext_url": null,
  "id": "70xx4yz7zs95a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19286",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7203871769",
  "pdf_url": "https://arxiv.org/pdf/2608.19286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70xx4yz7zs95a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.19286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Minimum attaining operators on reducing subspaces: Spectral structure and density",
  "title_text": "Minimum attaining operators on reducing subspaces: Spectral structure and density",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/70xx4yz7zs95a",
  "venue": "arXiv",
  "versions": []
}