{
  "abstract": "In this paper, we present an application of matrix-valued truncated Toeplitz operators to the matrix version of the Nevanlinna-Pick interpolation problem. We then investigate the unitary part of a matrix-valued truncated Toeplitz operator induced by a contractive matrix-valued symbol. We further prove that, for a pure matrix-valued inner function, the corresponding model space is invariant under multiplication operator if and only if the symbol is constant. In addition, we give an algebraic proof of a characterization of the invertibility of matrix-valued asymmetric truncated Toeplitz operators using Toeplitz operators with 2 by 2 block matrix symbol. We also discuss the solvability of matrix-valued asymmetric truncated Toeplitz operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15480",
  "author_total": 2,
  "authors": [
    {
      "name": "Rewayat Khan"
    },
    {
      "name": "Flavia Colonna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2be8yhxm3hjt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15480",
  "fulltext_url": null,
  "id": "d2be8yhxm3hjt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15480",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.15480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2be8yhxm3hjt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Matrix-Valued Truncated Toeplitz Operators: Properties and Applications",
  "title_text": "Matrix-Valued Truncated Toeplitz Operators: Properties and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/d2be8yhxm3hjt",
  "venue": "arXiv",
  "versions": []
}