{
  "id": "1205.2025",
  "version": "v1",
  "published": "2012-05-09T16:31:08.000Z",
  "updated": "2012-05-09T16:31:08.000Z",
  "title": "The numerical range of a contraction with finite defect numbers",
  "authors": [
    "Hari Bercovici",
    "Dan Timotin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "An n-dilation of a contraction T acting on a Hilbert space H is a unitary dilation acting on H \\oplus C^n. We show that if both defect numbers of T are equal to n, then the closure of the numerical range of T is the intersection of the closures of the numerical ranges of its n-dilations. We also obtain detailed information about the geometrical properties of the numerical range of T in case n=1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-09T16:31:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A20"
    ],
    "keywords": [
      "numerical range",
      "finite defect numbers",
      "contraction",
      "n-dilation",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2025B"
    }
  }
}