{
  "id": "0706.1484",
  "version": "v2",
  "published": "2007-06-11T14:30:40.000Z",
  "updated": "2007-06-15T18:42:11.000Z",
  "title": "Frames of subspaces and operators",
  "authors": [
    "Mariano A. Ruiz",
    "Demetrio Stojanoff"
  ],
  "comment": "21 pages, LaTeX; added references and comments about fusion frames",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces $\\mathcal{E} = \\{E_i \\}_{i\\in I}$ of a Hilbert space $\\mathcal{K}$ and a surjective $T\\in L(\\mathcal{K}, \\mathcal{H})$ in order that $\\{T(E_i)\\}_{i\\in I}$ is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J. A. Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames. Proc. Amer. Math. Soc. 134 (2006), 1031-1037], which related frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinament of a fusion frame is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-15T18:42:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "47A05"
    ],
    "keywords": [
      "orthonormal basis",
      "fusion frame",
      "oblique projections",
      "separable hilbert space",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1484R"
    }
  }
}