{
  "id": "1309.4950",
  "version": "v3",
  "published": "2013-09-19T12:21:31.000Z",
  "updated": "2014-10-16T07:57:57.000Z",
  "title": "Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces",
  "authors": [
    "Julio Becerra Guerrero",
    "Ginés López-Pérez",
    "Abraham Rueda Zoca"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1304.4397",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and, however, its unit ball still contains convex combinations of slices with diameter arbitrarily small, which improves in a optimal way the known results about the size of this kind of subsets in Banach spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-11T08:18:20.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-16T07:57:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex combinations",
      "extreme differences",
      "unit ball",
      "banach space containing isomorphic copies",
      "nonempty relatively weakly open subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4950B"
    }
  }
}