{
  "abstract": "In this article, we characterize when a Toeplitz operator and a Hankel operator on the vector-valued Hardy space are skew commutators of each other, and determine necessary and sufficient conditions under which their product is self-adjoint. These characterizations extend the results in \\cite{LZD}. In addition, we completely classify the skew commutators of the unilateral shift $S$, its adjoint $S^*$ and $S\\oplus S^*.$ We also characterize the class of bounded linear operators that have $S$, $S^*$ and $S\\oplus S^*$ as skew-commutators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04752",
  "author_total": 2,
  "authors": [
    {
      "name": "Priyanka Aroda"
    },
    {
      "name": "Santanu Dey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qcmnm6k1nx34.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04752",
  "fulltext_url": null,
  "id": "3qcmnm6k1nx34",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04752",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7211883957",
  "pdf_url": "https://arxiv.org/pdf/2609.04752",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qcmnm6k1nx34.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04752",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04752"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space",
  "title_text": "The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/3qcmnm6k1nx34",
  "venue": "arXiv",
  "versions": []
}