{
  "abstract": "In this paper, we introduce and investigate a new class of bounded linear operators on a Hilbert space, called the polynomially quasi-mth Helton class of operators of order m∈ℕ. This class is defined through a vanishing operator relation involving a polynomial perturbation of the Helton operator map, namely. 𝒫(𝒜)*Φ(ℬ;𝒜)m(ℐ)𝒫(𝒜)=0, for some nonconstant polynomial 𝒫, where Φ(ℬ;𝒜) denotes the Helton operator map given by Φ(ℬ;𝒜)(X)=ℬX−X𝒜, so that Φ(ℬ;𝒜)m(ℐ)=∑j=0m(−1)j(mj)ℬj𝒜m−j. This framework extends the classical Helton class and the quasi-Helton class of order m by incorporating polynomial operator relations. We establish several fundamental properties of this class and investigate its structural behavior. In particular, we obtain characterizations, study stability properties, and discuss connections with well-known operator classes such as m-isometric and m-symmetric operators. Our results provide a unified framework that highlights the interplay between polynomial operator expressions and quasi-Helton-type relations in operator theory.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Asma Al Rwaily"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwgxjd6031mj4.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0355301",
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  "id": "fwgxjd6031mj4",
  "issns": [
    "1932-6203"
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  "landing_url": "https://doi.org/10.1371/journal.pone.0355301",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ],
    [
      "plos",
      "/Earth sciences/Geography/Human geography/Human mobility"
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      "/Physical sciences/Mathematics/Algebra/Linear algebra/Eigenvectors"
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    [
      "plos",
      "/Physical sciences/Mathematics/Algebra/Polynomials"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Number theory/Complex numbers"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Operator theory"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Operator theory/Kernel functions"
    ],
    [
      "plos",
      "/Social sciences/Human geography/Human mobility"
    ]
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  "openalex": "W7206193372",
  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0355301&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/fwgxjd6031mj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "10.1371/journal.pone.0355301",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0355301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "plos:algebra",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Polynomially Quasi-mth-Helton class of Hilbert spaces operators",
  "title_text": "Polynomially Quasi-mth-Helton class of Hilbert spaces operators",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/fwgxjd6031mj4",
  "venue": "PLOS One",
  "versions": []
}