{
  "id": "1304.7068",
  "version": "v1",
  "published": "2013-04-26T05:29:16.000Z",
  "updated": "2013-04-26T05:29:16.000Z",
  "title": "Remarks on diameter 2 properties",
  "authors": [
    "Trond Abrahamsen",
    "Vegard Lima",
    "Olav Nygaard"
  ],
  "comment": "To appear in Journal of Convex Analysis",
  "categories": [
    "math.FA"
  ],
  "abstract": "If $X$ is an infinite-dimensional uniform algebra, if $X$ has the Daugavet property or if $X$ is a proper $M$-embedded space, every relatively weakly open subset of the unit ball of the Banach space $X$ is known to have diameter 2, i.e., $X$ has the diameter 2 property. We prove that in these three cases even every finite convex combination of relatively weakly open subsets of the unit ball have diameter 2. Further, we identify new examples of spaces with the diameter 2 property outside the formerly known cases; in particular we observe that forming $\\ell_p$-sums of diameter 2 spaces does not ruin diameter 2 structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-26T05:29:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B22"
    ],
    "keywords": [
      "relatively weakly open subset",
      "unit ball",
      "infinite-dimensional uniform algebra",
      "finite convex combination",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7068A"
    }
  }
}