{
  "abstract": "We study multipliers Mm,f,g of continuous K-frames over a σ-finite measure space. We give criteria for invertibility on Ran(K) governed by ∥m−1∥∞, and show that previously published criteria stated in terms of ∥m∥∞ have hypotheses that no admissible data can satisfy, so that they are vacuous rather than false. A Douglas-type characterization replaces the known one: Mm,f,g is invertible on Ran(K) exactly when Ran(K)⊆Ran(πRan(K)Mm¯,g,f). We then characterize the existence of continuous K-right and K-left inverses by range inclusions, identify those of minimal norm, and represent one-sided inverses as multipliers of continuous K-duals; a two-dimensional example shows that a representation formula for K-left inverses previously stated in the discrete setting is not correct as stated. Finally, we prove that pointwise biorthogonality is ineffective when μ has no atoms, and replace it by a μ-weighted biorthogonality along a partition of Ω into blocks, which we then extend to families that are not constant on the blocks.",
  "abstract_shown": true,
  "affiliations": [
    "Laboratory Analysis, Geometry and Applications, University of Ibn Tofail, Kenitra 14000, Morocco",
    "Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Khadija Mabrouk"
    },
    {
      "affs": [
        1
      ],
      "name": "Maryam Gharamah Alshehri"
    },
    {
      "affs": [
        0
      ],
      "name": "Mohamed Rossafi",
      "orcid": "0000-0002-5662-6921"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwxe0ejvys3d0.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203794",
  "fulltext_url": null,
  "id": "fwxe0ejvys3d0",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3794",
  "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",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7222968551",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/fwxe0ejvys3d0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203794",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematical Analysis and Transform Methods",
      "subfield": "general"
    }
  ],
  "title": "Multipliers of Continuous K-Frames",
  "title_text": "Multipliers of Continuous K-Frames",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/fwxe0ejvys3d0",
  "venue": "Mathematics",
  "versions": []
}