{
  "id": "math/9302208",
  "version": "v1",
  "published": "1993-02-04T16:55:49.000Z",
  "updated": "1993-02-04T16:55:49.000Z",
  "title": "Every nonreflexive subspace of L_1[0,1] fails the fixed point property",
  "authors": [
    "Paddy N. Dowling",
    "Christopher J. Lennard"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The main result of this paper is that every non-reflexive subspace $Y$ of $L_1[0,1]$ fails the fixed point property for closed, bounded, convex subsets $C$ of $Y$ and nonexpansive (or contractive) mappings on $C$. Combined with a theorem of Maurey we get that for subspaces $Y$ of $L_1[0,1]$, $Y$ is reflexive if and only if $Y$ has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-02-04T16:55:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed point property",
      "nonreflexive subspace",
      "general banach spaces",
      "main result",
      "convex subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......2208D"
    }
  }
}