{
  "id": "1202.0503",
  "version": "v1",
  "published": "2012-02-02T17:51:07.000Z",
  "updated": "2012-02-02T17:51:07.000Z",
  "title": "A characterisation of inner product spaces by the maximal circumradius of spheres",
  "authors": [
    "Sebastian Scholtes"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.MG"
  ],
  "abstract": "We give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal cirumradius of spheres. It turns out that a normed vector space $(X,\\norm{\\cdot})$ with $\\dim X\\geq 2$ is an inner product space if and only if all spheres are not degenerate, i.e. the maximal circumradius of points on the sphere equals the radius of the sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-02T17:51:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C15",
      "46B20"
    ],
    "keywords": [
      "inner product space",
      "maximal circumradius",
      "normed vector space",
      "characterisation",
      "sphere equals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0503S"
    }
  }
}