{
  "id": "0811.4234",
  "version": "v1",
  "published": "2008-11-26T07:11:09.000Z",
  "updated": "2008-11-26T07:11:09.000Z",
  "title": "A non-smooth continuous unitary representation of a Banach-Lie group",
  "authors": [
    "Daniel Beltita",
    "Karl-Hermann Neeb"
  ],
  "comment": "5 pages",
  "categories": [
    "math.RT",
    "math.FA"
  ],
  "abstract": "In this note we show that the representation of the additive group of the Hilbert space $L^2([0,1],\\R)$ on $L^2([0,1],\\C)$ given by the multiplication operators $\\pi(f) := e^{if}$ is continuous but its space of smooth vectors is trivial. This example shows that a continuous unitary representation of an infinite dimensional Lie group need not be smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-26T07:11:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E65",
      "22E45"
    ],
    "keywords": [
      "non-smooth continuous unitary representation",
      "banach-lie group",
      "infinite dimensional lie group",
      "smooth vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4234B"
    }
  }
}