{
  "id": "1111.2273",
  "version": "v2",
  "published": "2011-11-09T16:58:41.000Z",
  "updated": "2013-04-24T12:54:04.000Z",
  "title": "Equilateral sets in infinite dimensional Banach spaces",
  "authors": [
    "S. K. Mercourakis",
    "G. Vassiliadis"
  ],
  "comment": "to appear in Proc. Am. Math. Soc. (9 pages, no figures)",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We show that every Banach space $X$ containing an isomorphic copy of $c_0$ has an infinite equilateral set and also that if $X$ has a bounded biorthogonal system of size $\\alpha$ then it can be renormed so as to admit an equilateral set of equal size. If $K$ is any compact non metrizable space, then under a certain combinatorial condition on $K$ the Banach space $C(K)$ has an uncountable equilateral set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-24T12:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B26",
      "46B04"
    ],
    "keywords": [
      "infinite dimensional banach spaces",
      "infinite equilateral set",
      "compact non metrizable space",
      "uncountable equilateral set",
      "combinatorial condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2273M"
    }
  }
}