{
  "id": "1301.3396",
  "version": "v5",
  "published": "2013-01-15T16:14:52.000Z",
  "updated": "2014-01-13T18:12:31.000Z",
  "title": "Stability of Banach spaces via nonlinear $\\varepsilon$-isometries",
  "authors": [
    "Duanxu Dai",
    "Yunbai Dong"
  ],
  "comment": "17 pages, accepted by J. Math. Anal. Appl",
  "journal": "J.Math.Anal.Appl. 414 (2014) 996-1005",
  "doi": "10.1016/j.jmaa.2014.01.028",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we prove that the existence of an $\\varepsilon$-isometry from a separable Banach space $X$ into $Y$ (the James space or a reflexive space) implies the existence of a linear isometry from $X$ into $Y$. Then we present a set valued mapping version lemma on non-surjective $\\varepsilon$-isometries of Banach spaces. Using the above results, we also discuss the rotundity and smoothness of Banach spaces under the perturbation by $\\varepsilon$-isometries.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-01-13T18:12:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "26E25",
      "54C65",
      "54C60"
    ],
    "keywords": [
      "set valued mapping version lemma",
      "separable banach space",
      "linear isometry",
      "james space",
      "reflexive space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3396D"
    }
  }
}