{
  "id": "1801.02002",
  "version": "v1",
  "published": "2018-01-06T10:58:11.000Z",
  "updated": "2018-01-06T10:58:11.000Z",
  "title": "Antipodal sets in infinite dimensional Banach spaces",
  "authors": [
    "Eftychios Glakousakis",
    "Sophocles Mercourakis"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "The following strengthening of the Elton-Odell theorem on the existence of a $(1+\\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\\subseteq S_X$ and a constant $d>1$, satisfying the property that for every $x,y\\in S$ with $x\\neq y$ there exists $f\\in B_{X^*}$ such that $d\\leq f(x)-f(y)$ and $f(y)\\leq f(z)\\leq f(x)$, for all $z\\in S$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-06T10:58:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite dimensional banach space",
      "antipodal sets",
      "infinite subset",
      "unit sphere",
      "elton-odell theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}