{
  "id": "math/0702216",
  "version": "v1",
  "published": "2007-02-08T11:22:01.000Z",
  "updated": "2007-02-08T11:22:01.000Z",
  "title": "A Decomposition Theorem for frames and the Feichtinger Conjecture",
  "authors": [
    "Peter G. Casazza",
    "Gitta Kutyniok",
    "Darrin Speegle",
    "Janet C. Tremain"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is $\\omega$-independent for $\\ell_2$-sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-08T11:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C05",
      "42C15",
      "46L05"
    ],
    "keywords": [
      "feichtinger conjecture",
      "decomposition theorem",
      "unit norm bessel sequence",
      "finite union",
      "finite orthogonal decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2216C"
    }
  }
}