{
  "id": "math/0508646",
  "version": "v2",
  "published": "2005-08-31T17:12:32.000Z",
  "updated": "2005-09-02T17:35:23.000Z",
  "title": "The Schur-Horn theorem for operators and frames with prescribed norms and frame operator",
  "authors": [
    "J. Antezana",
    "P. Massey",
    "M. Ruiz",
    "D. Stojanoff"
  ],
  "comment": "To appear in Illinois Journal of Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\\mathcal H$, and a bounded sequence $\\mathbf{c} = \\{c_k \\}_{k \\in \\mathbb N}$ of non negative real numbers, the pair $(S, \\mathbf{c})$ is frame admissible, if there exists a frame $\\{f_k \\}_{k \\in \\mathbb{N}} $ on $\\mathcal H$ with frame operator $S$, such that $\\|f_k \\|^2 = c_k$, $k \\in \\mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions (and to generalize known sufficient conditions) for a pair $(S, \\mathbf{c})$, to be frame admissible.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-02T17:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "47A05"
    ],
    "keywords": [
      "schur-horn theorem",
      "frame operator",
      "prescribed norms",
      "non negative real numbers",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8646A"
    }
  }
}