{
  "id": "math/9811148",
  "version": "v1",
  "published": "1998-11-24T19:20:22.000Z",
  "updated": "1998-11-24T19:20:22.000Z",
  "title": "Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations",
  "authors": [
    "Peter G. Casazza"
  ],
  "comment": "to appear: J. of Fourier Anal. and Appl's",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-24T19:20:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46C05"
    ],
    "keywords": [
      "orthonormal bases",
      "frame representations",
      "riesz basis",
      "larger hilbert space",
      "linear combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11148C"
    }
  }
}