{
  "id": "0801.2726",
  "version": "v2",
  "published": "2008-01-17T19:50:05.000Z",
  "updated": "2008-12-04T09:48:02.000Z",
  "title": "Schatten p-norm inequalities related to a characterization of inner product spaces",
  "authors": [
    "O. Hirzallah",
    "F. Kittaneh",
    "M. S. Moslehian"
  ],
  "comment": "Minor revision, to appear in Math. Inequal. Appl. (MIA)",
  "journal": "Math. Inequal. Appl. 13 (2010), no. 2, 235-241",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \\sum_{i=1}^n \\|A_i\\|^p_p \\leq \\sum_{i,j=1}^n\\|A_i\\pm A_j\\|^p_p for $0<p\\leq 2$, and the reverse inequality holds for $2\\leq p<\\infty$. Moreover, \\sum_{i,j=1}^n\\|A_i\\pm A_j\\|^2_p \\leq 2n^{2/p} \\sum_{i=1}^n \\|A_i\\|^2_p for $0<p\\leq 2$, and the reverse inequality holds for $2\\leq p<\\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-04T09:48:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C15",
      "47A30",
      "47B10",
      "47B15"
    ],
    "keywords": [
      "inner product spaces",
      "schatten p-norm inequalities",
      "reverse inequality holds",
      "characterization",
      "separable complex hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2726H"
    }
  }
}