{
  "id": "1903.03417",
  "version": "v1",
  "published": "2019-03-08T13:17:27.000Z",
  "updated": "2019-03-08T13:17:27.000Z",
  "title": "Power bounded $m$-left invertible operators",
  "authors": [
    "B. P. Duggal",
    "C. S. Kubrusly"
  ],
  "comment": "10",
  "categories": [
    "math.FA"
  ],
  "abstract": "A Hilbert space operator $S\\in\\B$ is left $m$-invertible by $T\\in\\B$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right)T^jS^j}=0,$$ $S$ is $m$-isometric if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jS^j}=0$$ and $S$ is $(m,C)$-isometric for some conjugation $C$ of $\\H$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jCS^jC}=0.$$ If a power bounded operator $S$ is left invertible by a power bounded operator $T$, then $S$ (also, $T^*$) is similar to an isometry. Translated to $m$-isometric and $(m,C)$-isometric operators $S$ this implies that $S$ is $1$-isometric, equivalently isometric, and (respectively) $(1,C)$-isometric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-08T13:17:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A55",
      "47A80",
      "47A10"
    ],
    "keywords": [
      "left invertible operators",
      "power bounded operator",
      "hilbert space operator",
      "isometric operators",
      "conjugation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}