{
  "id": "1301.4574",
  "version": "v1",
  "published": "2013-01-19T17:00:14.000Z",
  "updated": "2013-01-19T17:00:14.000Z",
  "title": "The Bishop-Phelps-Bollobás property for numerical radius in $\\ell_1(\\mathbb{C})$",
  "authors": [
    "Antonio J. Guirao",
    "Olena Kozhushkina"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop-Phelps-Bollob\\'as type theorem for numerical radius whenever $X$ is $\\ell_1(\\mathbb{C})$ or $c_0(\\mathbb{C})$. As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollob\\'as theorem for $\\ell_1(\\mathbb{C})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-19T17:00:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47A12"
    ],
    "keywords": [
      "numerical radius",
      "bishop-phelps-bollobás property",
      "bishop-phelps-bollobas type theorem",
      "essential tool",
      "bounded linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4574G"
    }
  }
}