{
  "id": "2407.20096",
  "version": "v1",
  "published": "2024-07-29T15:25:14.000Z",
  "updated": "2024-07-29T15:25:14.000Z",
  "title": "On best coapproximations in subspaces of diagonal matrices",
  "authors": [
    "Debmalya Sain",
    "Shamim Sohel",
    "Souvik Ghosh",
    "Kallol Paul"
  ],
  "journal": "Linear and Multilinear Algebra 71(1)(2021)47-62",
  "doi": "10.1080/03081087.2021.2017835",
  "categories": [
    "math.FA"
  ],
  "abstract": "We characterize the best coapproximation(s) to a given matrix $ T $ out of a given subspace $ \\mathbb{Y} $ of the space of diagonal matrices $ \\mathcal{D}_n $, by using Birkhoff-James orthogonality techniques and with the help of a newly introduced property, christened the $ * $-Property. We also characterize the coproximinal subspaces and the co-Chebyshev subspaces of $ \\mathcal{D}_n $ in terms of the $ * $-Property. We observe that a complete characterization of the best coapproximation problem in $ \\ell_{\\infty}^n $ follows directly as a particular case of our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T15:25:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47L05"
    ],
    "keywords": [
      "diagonal matrices",
      "birkhoff-james orthogonality techniques",
      "best coapproximation problem",
      "coproximinal subspaces",
      "co-chebyshev subspaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}