{
  "id": "1312.7698",
  "version": "v3",
  "published": "2013-12-30T12:50:44.000Z",
  "updated": "2014-04-01T11:37:55.000Z",
  "title": "On the Bishop-Phelps-Bollobás property for numerical radius",
  "authors": [
    "Sun Kwang Kim",
    "Han Ju Lee",
    "Miguel Martín"
  ],
  "journal": "Abstract and Applied Analysis, Volume 2014, Article ID 479208, 16 pages",
  "doi": "10.1155/2014/479208",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the Bishop-Phelps-Bollob\\'as property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces ensuring the BPBp-nu. Among other results, we show that $L_1(\\mu)$-spaces have this property for every measure $\\mu$. On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu. In particular, this shows that the Radon-Nikod\\'{y}m property (even reflexivity) is not enough to get BPBp-nu.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-01T11:37:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B04",
      "46B22"
    ],
    "keywords": [
      "numerical radius",
      "bishop-phelps-bollobás property",
      "infinite-dimensional separable banach space",
      "bishop-phelps-bollobas property",
      "sufficient conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.7698K"
    }
  }
}