{
  "id": "0711.1208",
  "version": "v2",
  "published": "2007-11-08T06:39:05.000Z",
  "updated": "2012-08-18T22:33:29.000Z",
  "title": "Finite dimensional subspaces of noncommutative $L_p$ spaces",
  "authors": [
    "Hun Hee Lee"
  ],
  "comment": "This paper has been withdrawn due to a crucial error in the proof of Proposition 3.2",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \\leq c_p n^{\\abs{1/2-1/p}} for some constant c_p depending only on $p$, where $1/p +1/p' =1$ and $RC^n_{p'} = [R_n\\cap C_n, R_n+C_n]_{1/p'}$. Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with $\\norm{P}_{cb} \\leq c_p n^{\\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-18T22:33:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L25",
      "46B07"
    ],
    "keywords": [
      "finite dimensional subspaces",
      "von neumann algebra",
      "n-dimensional subspace",
      "lewiss classical result",
      "density argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1208L"
    }
  }
}