{
  "id": "1207.0975",
  "version": "v2",
  "published": "2012-07-04T13:30:58.000Z",
  "updated": "2013-01-03T08:58:47.000Z",
  "title": "Can you compute the operator norm?",
  "authors": [
    "Tobias Fritz",
    "Tim Netzer",
    "Andreas Thom"
  ],
  "comment": "15 pages, no figures; v2 is a slightly revised version",
  "categories": [
    "math.FA",
    "math.GR"
  ],
  "abstract": "In this note we address various algorithmic problems that arise in the computation of the operator norm in unitary representations of a group on Hilbert space. We show that the operator norm in the universal unitary representation is computable if the group is residually finite-dimensional or amenable with decidable word problem. Moreover, we relate the computability of the operator norm on the product of non-abelian free groups to Kirchberg's QWEP Conjecture, a fundamental open problem in the theory of operator algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-03T08:58:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A20"
    ],
    "keywords": [
      "operator norm",
      "fundamental open problem",
      "kirchbergs qwep conjecture",
      "universal unitary representation",
      "non-abelian free groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0975F"
    }
  }
}