{
  "id": "1208.4266",
  "version": "v1",
  "published": "2012-08-21T13:47:40.000Z",
  "updated": "2012-08-21T13:47:40.000Z",
  "title": "Unitary invariants on the unit ball of B(H)^n",
  "authors": [
    "Gelu Popescu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we introduce a unitary invariant $\\Gamma$ defined on the unit ball of $B(H)^n$ in terms of the characteristic function, the noncommutative Poisson kernel, and the defect operator associated with a row contraction. We show that $\\Gamma$ detects the pure row isometries and completely classify them up to a unitary equivalence. We also show that $\\Gamma$ detects the pure row contractions with polynomial characteristic functions and completely non-coisometric row contractions. In particular, we show that any completely non-coisometric row contraction with constant characteristic function is homogeneous. Under a natural topology, we prove that the free holomorphic automorphism group of the unit ball of $B(H)^n$ is a metrizable, $\\sigma$-compact, locally compact group, and provide a concrete unitary projective representation of it in terms of noncommutative Poisson kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-21T13:47:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit ball",
      "unitary invariant",
      "non-coisometric row contraction",
      "noncommutative poisson kernel",
      "free holomorphic automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.4266P"
    }
  }
}