{
  "id": "1604.04858",
  "version": "v1",
  "published": "2016-04-17T10:25:56.000Z",
  "updated": "2016-04-17T10:25:56.000Z",
  "title": "Factorizations of Characteristic Functions",
  "authors": [
    "Kalpesh J. Haria",
    "Amit Maji",
    "Jaydeb Sarkar"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA",
    "math.CV",
    "math.OA"
  ],
  "abstract": "Let $A = (A_1, \\ldots, A_n)$ and $B = (B_1, \\ldots, B_n)$ be row contractions on $\\mathcal{H}_1$ and $\\mathcal{H}_2$, respectively, and $X$ be a row operator from $\\oplus_{i=1}^n \\mathcal{H}_2$ to $\\mathcal{H}_1$. Let $D_{A^*} = (I - A A^*)^{\\frac{1}{2}}$ and $D_{B} = (I - B^* B)^{\\frac{1}{2}}$ and $\\Theta_T$ be the characteristic function of $T = \\begin{bmatrix} A& D_{A^*}L D_B\\\\ 0 & B \\end{bmatrix}$. Then $\\Theta_T$ coincides with the product of the characteristic function $\\Theta_A$ of $A$, the Julia-Halmos matrix corresponding to $L$ and the characteristic function $\\Theta_B$ of $B$. More precisely, $\\Theta_T$ coincides with \\[ \\begin{bmatrix} \\Theta_B & 0 \\\\ 0 & I \\end{bmatrix} (I_\\Gamma \\otimes \\begin{bmatrix} L^* & (I - L^* L)^{\\frac{1}{2}} \\\\ (I - L L^*)^{\\frac{1}{2}} & - L \\end{bmatrix}) \\begin{bmatrix} \\Theta_A & 0\\\\ 0& I\\end{bmatrix}, \\] where $\\Gamma$ is the full Fock space. Similar results hold for constrained row contractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-17T10:25:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A13",
      "47A15",
      "47A20",
      "47A68"
    ],
    "keywords": [
      "characteristic function",
      "factorizations",
      "similar results hold",
      "full fock space",
      "row operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404858H"
    }
  }
}