{
  "id": "2305.00859",
  "version": "v1",
  "published": "2023-05-01T14:59:56.000Z",
  "updated": "2023-05-01T14:59:56.000Z",
  "title": "A Bishop-Phelps-Bollobas theorem for disc algebra",
  "authors": [
    "Neeru Bala",
    "Jaydeb Sarkar",
    "Aryaman Sensarma"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA",
    "math.CV",
    "math.OA"
  ],
  "abstract": "Let $\\mathbb{D}$ represent the open unit disc in $\\mathbb{C}$. Denote by $A(\\mathbb{D})$ the disc algebra, and $\\mathscr{B}(X, A(\\mathbb{\\mathbb{D}}))$ the Banach space of all bounded linear operators from a Banach space $X$ into $A(\\mathbb{D})$. We prove that, under the assumption of equicontinuity at a point in $\\partial \\mathbb{D}$, the Bishop-Phelps-Bollob\\'{a}s property holds for $\\mathscr{B}(X, A(\\mathbb{\\mathbb{D}}))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-01T14:59:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E15",
      "46E22",
      "46H10",
      "30H05",
      "47L20",
      "46J10"
    ],
    "keywords": [
      "disc algebra",
      "bishop-phelps-bollobas theorem",
      "banach space",
      "open unit disc",
      "bounded linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}