{
  "id": "0908.1942",
  "version": "v2",
  "published": "2009-08-13T17:45:54.000Z",
  "updated": "2009-08-15T12:06:56.000Z",
  "title": "Orthonormal bases of Hilbert spaces",
  "authors": [
    "Ilijas Farah"
  ],
  "comment": "The main result of the note has been known. See Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces D. Buhagiar, E. Chetcuti, H. Weber, J. Math. Anal. Appl., 345 (2008) 725-730. and the references thereof. Thanks to Nigel Kalton to pointing this out",
  "categories": [
    "math.LO",
    "math.FA"
  ],
  "abstract": "I prove that a Hilbert space has the property that each of its dense (not necessarily closed) subspaces contains an orthoormal basis if and only if it is separable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-15T12:06:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert space",
      "orthonormal bases",
      "subspaces contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.1942F"
    }
  }
}