{
  "id": "math/0605251",
  "version": "v1",
  "published": "2006-05-10T08:12:41.000Z",
  "updated": "2006-05-10T08:12:41.000Z",
  "title": "Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra",
  "authors": [
    "Uffe Haagerup",
    "Hanne Schultz"
  ],
  "comment": "50 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R-diagonal operators in this class. As a particular case, we determine the Brown measure of z=xy^{-1}, where (x,y) is a circular system in the sense of Voiculescu, and we prove that for all positive integers n, z^n is in L^p(M) iff 0<p< 2/(n+1).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-10T08:12:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L54",
      "47C15",
      "60B99"
    ],
    "keywords": [
      "finite von neumann algebra",
      "brown measure",
      "unbounded operators",
      "generalize browns spectral distribution measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5251H"
    }
  }
}