{
  "id": "1902.08492",
  "version": "v1",
  "published": "2019-02-22T13:49:45.000Z",
  "updated": "2019-02-22T13:49:45.000Z",
  "title": "Some examples of $m$-isometries",
  "authors": [
    "T. Bermúdez",
    "A. Martinón",
    "H. Zaway"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We obtain the admissible sets on the unit circle to be the spectrum of a strict $m$-isometry on an $n$-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an $m$-isometry. We determine that the only $m$-isometries on $\\mathbb{R}^2$ are $3$-isometries and isometries giving by $\\pm I+Q$, where $Q$ is a nilpotent operator. Moreover, on real Hilbert space, we obtain that $m$-isometries preserve volumes. Also we present a way to construct a strict $(m+1)$-isometry with an $m$-isometry given, using ideas of Aleman and Suciu \\cite[Proposition 5.2]{AS} on infinite dimensional Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-22T13:49:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite dimensional hilbert space",
      "real hilbert space",
      "isometries preserve volumes",
      "better picture",
      "correct spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}