{
  "id": "1409.5898",
  "version": "v1",
  "published": "2014-09-20T15:15:16.000Z",
  "updated": "2014-09-20T15:15:16.000Z",
  "title": "Le problème de Kadison-Singer (The Kadison-Singer problem)",
  "authors": [
    "Alain Valette"
  ],
  "comment": "S\\'eminaire Bourbaki, Juin 2014; 66\\`eme ann\\'ee, 2013-2014; $n^o$ 1088. To appear in Ast\\'erisque, in French",
  "categories": [
    "math.FA"
  ],
  "abstract": "In 1959, R.V. Kadison and I.M. Singer asked whether each pure state of the algebra of bounded diagonal operators on $\\ell^2$, admits a unique state extension to $B(\\ell^2)$. The positive answer was given in June 2013 by A. Marcus, D. Spielman and N. Srivastava, who took advantage of a series of translations of the original question, due to C. Akemann, J. Anderson, N. Weaver,... Ultimately, the problem boils down to an estimate of the largest zero of the expected characteristic polynomial of the sum of independent random variables taking values in rank 1 positive matrices in the algebra of n-by-n matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-20T15:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A15",
      "26C10",
      "46L30"
    ],
    "keywords": [
      "kadison-singer problem",
      "independent random variables",
      "unique state extension",
      "n-by-n matrices",
      "pure state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5898V"
    }
  }
}