{
  "id": "2010.02615",
  "version": "v1",
  "published": "2020-10-06T10:53:54.000Z",
  "updated": "2020-10-06T10:53:54.000Z",
  "title": "The Bishop-Phelps-Bollobás property on the space of $c_0$-sum",
  "authors": [
    "Geunsu Choi",
    "Sun Kwang Kim"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main purpose of this paper is to study Bishop-Phelps-Bollob\\'as type properties on $c_0$ sum of Banach spaces. Among other results, we show that the pair $(c_0(X),Y)$ has the Bishop-Phelps-Bollob\\'as property (in short, BPBp) for operators whenever $X$ is uniformly convex and $Y$ is (complex) uniformly convex. We also prove that the pair $(c_0(X),c_0(X))$ has the BPBp for bilinear forms whenever $X$ is both uniformly convex and uniformly smooth. These extend the previously known results that $(c_0,Y)$ has the BPBp for operators whenever $Y$ is uniformly convex and $(c_0,c_0)$ has the BPBp for bilinear forms. We also obtain some results on a local BPBp which is called $\\mathbf{L}_{p,p}$ for both operators and bilinear forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-06T10:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B07",
      "46B20"
    ],
    "keywords": [
      "bishop-phelps-bollobás property",
      "uniformly convex",
      "bilinear forms",
      "study bishop-phelps-bollobas type properties",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}