{
  "id": "2001.02490",
  "version": "v1",
  "published": "2020-01-08T13:08:54.000Z",
  "updated": "2020-01-08T13:08:54.000Z",
  "title": "Isometric actions on Lp-spaces: dependence on the value of p",
  "authors": [
    "Amine Marrakchi",
    "Mikael de la Salle"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR",
    "math.FA"
  ],
  "abstract": "We prove that, for every topological group $G$, the following two sets are intervals: the set of real numbers $p > 0$ such that every continuous action of $G$ by isometries on an $L_p$ space has bounded orbits, and the set of $p > 0$ such that $G$ admits a metrically proper continuous action by isometries on an $L_p$ space. This answers a question by Chatterji--Drutu--Haglund.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T13:08:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isometric actions",
      "dependence",
      "real numbers",
      "isometries",
      "metrically proper continuous action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}