{
  "id": "math/9512204",
  "version": "v1",
  "published": "1995-12-06T00:00:00.000Z",
  "updated": "1995-12-06T00:00:00.000Z",
  "title": "On isometric reflexions in Banach spaces",
  "authors": [
    "A. Skorik",
    "Mikhail Zaidenberg"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We obtain the following characterization of Hilbert spaces. Let $E$ be a Banach space whose unit sphere $S$ has a hyperplane of symmetry. Then $E$ is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group ${\\rm Iso}\\, E$ of $E$ has a dense orbit in S; b) the identity component $G_0$ of the group ${\\rm Iso}\\, E$ endowed with the strong operator topology acts topologically irreducible on $E$. Some related results on infinite dimentional Coxeter groups generated by isometric reflexions are given which allow to analyse the structure of isometry groups containing sufficiently many reflexions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-12-06T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach space",
      "isometric reflexions",
      "dimentional coxeter groups",
      "operator topology acts",
      "topology acts topologically irreducible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math.....12204S"
    }
  }
}