{
  "id": "1309.0689",
  "version": "v1",
  "published": "2013-09-03T14:16:23.000Z",
  "updated": "2013-09-03T14:16:23.000Z",
  "title": "Subnormal weighted shifts on directed trees and composition operators in $L^2$ spaces with non-densely defined powers",
  "authors": [
    "Piotr Budzynski",
    "Piotr Dymek",
    "Zenon Jan Jablonski",
    "Jan Stochel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is shown that for every positive integer $n$ there exists a subnormal weighted shift on a directed tree (with or without root) whose $n$th power is densely defined while its $(n+1)$th power is not. As a consequence, for every positive integer $n$ there exists a non-symmetric subnormal composition operator $C$ in an $L^2$ space over a $\\sigma$-finite measure space such that $C^n$ is densely defined and $C^{n+1}$ is not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-03T14:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B20",
      "47B37",
      "47B33"
    ],
    "keywords": [
      "subnormal weighted shift",
      "non-densely defined powers",
      "directed tree",
      "non-symmetric subnormal composition operator",
      "th power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0689B"
    }
  }
}