{
  "id": "2407.20102",
  "version": "v1",
  "published": "2024-07-29T15:29:43.000Z",
  "updated": "2024-07-29T15:29:43.000Z",
  "title": "On the best coapproximation problem in $\\ell_1^n$",
  "authors": [
    "Debmalya Sain",
    "Shamim Sohel",
    "Souvik Ghosh",
    "Kallol Paul"
  ],
  "journal": "Linear and Multilinear Algebra 72(1)(2022)31-49",
  "doi": "10.1080/03081087.2022.2153101",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the best coapproximation problem in the Banach space $ \\ell_1^n, $ by using Birkhoff-James orthogonality techniques. Given a subspace $\\mathbb{{Y}}$ of $\\ell_1^n$, we completely identify the elements $x$ in $\\ell_1^n,$ for which best coapproximations to $x$ out of $\\mathbb{{Y}}$ exist. The methods developed in this article are computationally effective and it allows us to present an algorithmic approach to the concerned problem. We also identify the coproximinal subspaces and co-Chebyshev subspaces of $\\ell_1^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T15:29:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47L05"
    ],
    "keywords": [
      "best coapproximation problem",
      "birkhoff-james orthogonality techniques",
      "banach space",
      "co-chebyshev subspaces",
      "coproximinal subspaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}