{
  "id": "1009.0079",
  "version": "v1",
  "published": "2010-09-01T02:53:40.000Z",
  "updated": "2010-09-01T02:53:40.000Z",
  "title": "A characterization of inner product spaces",
  "authors": [
    "Mohammad Sal Moslehian",
    "John M. Rassias"
  ],
  "comment": "8 Pages, to appear in Kochi J. Math. (Japan)",
  "journal": "Kochi J. Math. 6 (2011), 101-107",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \\|...\\|)$ is an inner product space if $$\\sum_{\\epsilon_i \\in \\{-1,1\\}} \\|x_1 + \\sum_{i=2}^k\\epsilon_ix_i\\|^2=\\sum_{\\epsilon_i \\in \\{-1,1\\}} (\\|x_1\\| + \\sum_{i=2}^k\\epsilon_i\\|x_i\\|)^2,$$ for some positive integer $k\\geq 2$ and all $x_1, ..., x_k \\in X$. Conversely, if $(X, \\|...\\|)$ is an inner product space, then the equality above holds for all $k\\geq 2$ and all $x_1, ..., x_k \\in X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-01T02:53:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C15",
      "46B20",
      "46C05"
    ],
    "keywords": [
      "characterization",
      "real inner product spaces",
      "real normed space",
      "positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0079S"
    }
  }
}