{
  "id": "math/0512551",
  "version": "v1",
  "published": "2005-12-23T19:11:10.000Z",
  "updated": "2005-12-23T19:11:10.000Z",
  "title": "Characteristic functions and joint invariant subspaces",
  "authors": [
    "Gelu Popescu"
  ],
  "comment": "35 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a \"one-to-one\" correspondence between the joint invariant subspaces under T_1,..., T_n, and the regular factorizations of the characteristic function associated with T. In particular, we prove that there is a non-trivial joint invariant subspace under the operators T_1,..., T_n, if and only if there is a non-trivial regular factorization of the characteristic function. We also provide a functional model for the joint invariant subspaces in terms of the regular factorizations of the characteristic function, and prove the existence of joint invariant subspaces for certain classes of n-tuples of operators. We obtain criterions for joint similarity of n-tuples of operators to Cuntz row isometries. In particular, we prove that a completely non-coisometric row contraction T is jointly similar to a Cuntz row isometry if and only if the characteristic function of T is an invertible multi-analytic operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-23T19:11:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A20",
      "47A15"
    ],
    "keywords": [
      "characteristic function",
      "cuntz row isometry",
      "non-coisometric row contraction",
      "non-trivial joint invariant subspace",
      "non-trivial regular factorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12551P"
    }
  }
}