{
  "id": "1803.04727",
  "version": "v1",
  "published": "2018-03-13T11:01:18.000Z",
  "updated": "2018-03-13T11:01:18.000Z",
  "title": "Characterization of Banach spaces $Y$ satisfying that the pair $ (\\ell_\\infty^4,Y )$ has the Bishop-Phelps-Bollobás property for operators",
  "authors": [
    "María D. Acosta",
    "José L. Dávila",
    "Maryam Soleimani-Mourchehkhorti"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the Bishop-Phelps-Bollob\\'as property for operators from $\\ell_\\infty ^4 $ to a Banach space. For this reason we introduce an appropiate geometric property, namely the AHSp-$\\ell_\\infty ^4$. We prove that spaces $Y$satisfying AHSp-$\\ell_\\infty ^4$ are precisely those spaces $Y$ such that $(\\ell_\\infty^4,Y)$ has the Bishop-Phelps-Bollob\\'as property. We also provide classes of Banach spaces satisfying this condition. For instance, finite-dimensional spaces, uniformly convex spaces, $C_0(L)$ and $L_1 (\\mu)$ satisfy AHSp-$\\ell_\\infty ^4 $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T11:01:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47B99"
    ],
    "keywords": [
      "bishop-phelps-bollobás property",
      "characterization",
      "bishop-phelps-bollobas property",
      "appropiate geometric property",
      "uniformly convex spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}