{
  "id": "1207.1199",
  "version": "v2",
  "published": "2012-07-05T09:17:47.000Z",
  "updated": "2012-07-13T09:01:48.000Z",
  "title": "An obstruction to $\\ell^p$-dimension",
  "authors": [
    "Nicolas Monod",
    "Henrik Densing Petersen"
  ],
  "comment": "5 pages (cosmetic changes wrt v1)",
  "categories": [
    "math.GR",
    "math.FA"
  ],
  "abstract": "For any group $G$ containing an infinite elementary amenable subgroup, and any $2<p<\\infty$, there exists closed invariant subspaces $E_i\\nearrow \\ell^pG$ and $F\\neq 0$ such that $E_i\\cap F = 0$ for all $i$. This is an obstacle to $\\ell^p$-dimension and gives a negative answer to a question of Gaboriau.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-13T09:01:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "obstruction",
      "infinite elementary amenable subgroup",
      "closed invariant subspaces",
      "negative answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.1199M"
    }
  }
}