{
  "id": "1009.2249",
  "version": "v2",
  "published": "2010-09-12T17:03:35.000Z",
  "updated": "2010-12-02T19:18:11.000Z",
  "title": "Numerical ranges of $C_0(N)$ contractions",
  "authors": [
    "Chafiq Benhida",
    "Pamela Gorkin",
    "Dan Timotin"
  ],
  "comment": "v1: 13 pages; v2: 14 pages; typos removed, title changed, slight change to the proof of Theorem 4.6. The final publication will be available in IEOT at http://www.springerlink.com",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical ranges of all its unitary dilations. We show that for $C_0(N)$ contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-02T19:18:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A20"
    ],
    "keywords": [
      "numerical range",
      "contraction",
      "finite dimensional result",
      "li states",
      "intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2249B"
    }
  }
}