{
  "id": "1407.4768",
  "version": "v2",
  "published": "2014-07-17T18:35:49.000Z",
  "updated": "2015-01-05T17:21:56.000Z",
  "title": "Consequences of the Marcus/Spielman/Stivastava solution to the Kadison-Singer Problem",
  "authors": [
    "Peter G. Casazza"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:math/0510024",
  "categories": [
    "math.FA"
  ],
  "abstract": "It is known that the famous, intractible 1959 Kadison-Singer problem in $C^{*}$-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. The recent surprising solution to this problem by Marcus, Spielman and Srivastava was a significant achievement and a significant advance for all these areas of research. We will look at many of the known equivalent forms of the Kadison-Singer Problem and see what are the best new theorems available in each area of research as a consequence of the work of Marcus, Spielman and Srivastave. In the cases where {\\it constants} are important for the theorem, we will give the best constants available in terms of a {\\it generic constant} taken from \\cite{MSS}. Thus, if better constants eventually become available, it will be simple to adapt these new constants to the theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-17T18:35:49.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-05T17:21:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A05",
      "42A10",
      "42A16",
      "43A50",
      "46B03",
      "46B07",
      "46L05"
    ],
    "keywords": [
      "kadison-singer problem",
      "marcus/spielman/stivastava solution",
      "consequence",
      "significant achievement",
      "fundamental unsolved problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4768C"
    }
  }
}