{
  "id": "1703.04750",
  "version": "v1",
  "published": "2017-03-14T22:11:31.000Z",
  "updated": "2017-03-14T22:11:31.000Z",
  "title": "Lyapunov's Theorem for continuous frames",
  "authors": [
    "Marcin Bownik"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Akemann and Weaver (2014) have shown a remarkable extension of Weaver's $KS_r$ Conjecture (2004) in the form of approximate Lyapunov's theorem. This was made possible thanks to the breakthrough solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava (2015). In this paper we show a similar type of Lyapunov theorem for continuous frames on non-atomic measure spaces. In contrast with discrete frames, the proof of this result does not rely on the recent solution of the Kadison-Singer problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-14T22:11:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous frames",
      "kadison-singer problem",
      "approximate lyapunovs theorem",
      "non-atomic measure spaces",
      "discrete frames"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}