{
  "abstract": "We develop a semi-inner product framework for 2×2 block operator matrices acting on the direct sum K=H⊕H of a complex Hilbert space H, generated by the diagonal operator matrix A=diag(A,B), where A and B are distinct positive operators acting on H, neither assumed to be injective. This extends the setting of Bhunia, Paul, and Nayak [Electron. J. Linear Algebra 36 (2020), 143–157], who treated the case A=diag(A,A) with A injective. Using Douglas’ majorization theorem, we employ and develop the mixed (A,B)- and (B,A)-adjoint formalism in the block operator matrix setting; these adjoints relate the two distinct seminorms induced by A and B and take the place of the ordinary adjoint when these seminorms differ. Within this framework, we establish upper and lower bounds for the A-numerical radius of 2×2 operator matrices belonging to the appropriate A-bounded or A-adjointable classes, extending and refining the bounds of the above-mentioned paper to the case of two distinct, not necessarily injective, positive generators.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia",
    "Department of Mathematics, College of Science and Arts, Najran University, Najran 66462, Saudi Arabia",
    "Science and Engineering Research Center, Najran University, Najran, Saudi Arabia",
    "Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Amani Baazem"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Kais Feki",
      "orcid": "0000-0002-9326-4173"
    },
    {
      "affs": [
        3
      ],
      "name": "Hala H. Taha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/589c35v8fa39h.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214048",
  "fulltext_url": null,
  "id": "589c35v8fa39h",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4048",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/589c35v8fa39h.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:47Z",
      "native_id": "10.3390/math14214048",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "A Mixed-Adjoint Framework for 2 × 2 Operator Matrices and Their Numerical Radii",
  "title_text": "A Mixed-Adjoint Framework for 2 × 2 Operator Matrices and Their Numerical Radii",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T12:20:57Z",
  "url": "https://research.draconitic.com/paper/589c35v8fa39h",
  "venue": "Mathematics",
  "versions": []
}