{
  "id": "0901.1512",
  "version": "v2",
  "published": "2009-01-12T08:04:26.000Z",
  "updated": "2010-01-29T11:13:24.000Z",
  "title": "Isometries on extremely non-complex Banach spaces",
  "authors": [
    "Piotr Koszmider",
    "Miguel Martin",
    "Javier Meri"
  ],
  "comment": "18 pages, revised version, to appear in J. Inst. Math. Jussieu",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Given a separable Banach space $E$, we construct an extremely non-complex Banach space (i.e. a space satisfying that $\\|Id + T^2\\|=1+\\|T^2\\|$ for every bounded linear operator $T$ on it) whose dual contains $E^*$ as an $L$-summand. We also study surjective isometries on extremely non-complex Banach spaces and construct an example of a real Banach space whose group of surjective isometries reduces to $\\pm Id$, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-29T11:13:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B10",
      "46B20",
      "46E15",
      "47A99"
    ],
    "keywords": [
      "extremely non-complex banach space",
      "dual contains",
      "real banach space",
      "separable infinite-dimensional hilbert space",
      "study surjective isometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}