{
  "id": "1802.02857",
  "version": "v1",
  "published": "2018-02-08T13:59:03.000Z",
  "updated": "2018-02-08T13:59:03.000Z",
  "title": "Dimension dependence of factorization problems: Hardy spaces and $SL_n^\\infty$",
  "authors": [
    "Richard Lechner"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Given $1 \\leq p < \\infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $SL_n^\\infty$. We prove the following quantitative result: The identity operator on $W_n$ factors through any operator $T : W_N\\to W_N$ which has large diagonal with respect to the Haar system, where $N$ depends \\emph{linearly} on $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-08T13:59:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B07",
      "30H10",
      "46B25",
      "60G46"
    ],
    "keywords": [
      "factorization problems",
      "dimension dependence",
      "finite-dimensional dyadic hardy space",
      "identity operator",
      "large diagonal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}