{
  "id": "math/0611256",
  "version": "v1",
  "published": "2006-11-09T06:35:36.000Z",
  "updated": "2006-11-09T06:35:36.000Z",
  "title": "Invariant Subspaces for Operators in a General II_1-factor",
  "authors": [
    "Uffe Haagerup",
    "Hanne Schultz"
  ],
  "comment": "83 pages",
  "categories": [
    "math.OA",
    "math.FA"
  ],
  "abstract": "It is shown that to every operator T in a general von Neumann factor M of type II_1 and to every Borel set B in the complex plane, one can associate a largest, closed, T-invariant subspace, K = K_T(B), affiliated with M, such that the Brown measure of T|_K is concentrated on B. Moreover, K is T-hyperinvariant, and the Brown measure of (1-P_K)T|_(1-P_K)(H) is concentrated on C\\B. In particular, if T has a Brown measure which is not concentrated on a singleton, then there exists a non-trivial, closed, T-hyperinvariant subspace. Furthermore, it is shown that for every T in M, the limit A=\\lim_{n\\to\\infty}[(T^n)* T^n]^{1/2n} exists in the strong operator topology and K_T(\\bar{B(0,r)})=1_{[0,r]}(A), r>0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-09T06:35:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "47C15",
      "46L54"
    ],
    "keywords": [
      "invariant subspaces",
      "brown measure",
      "general von neumann factor",
      "strong operator topology",
      "t-invariant subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 83,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11256H"
    }
  }
}