{
  "id": "1906.05215",
  "version": "v1",
  "published": "2019-06-12T15:39:17.000Z",
  "updated": "2019-06-12T15:39:17.000Z",
  "title": "m-isometric operators and their local properties",
  "authors": [
    "Z. J. Jablonski",
    "I. B. Jung",
    "J. Stochel"
  ],
  "comment": "19 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an $m$-isometry for an unspecified $m$ written in terms of conditions that are applied to \"one vector at a time\". We provide criteria for orthogonality of generalized eigenvectors of an (a priori unbounded) linear operator $T$ on an inner product space that correspond to distinct eigenvalues of modulus 1. We also discuss a similar question of when Jordan blocks of $T$ corresponding to distinct eigenvalues of modulus 1 are \"orthogonal\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-12T15:39:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B20",
      "47A75"
    ],
    "keywords": [
      "local properties",
      "m-isometric operators",
      "bounded linear hilbert space operator",
      "distinct eigenvalues",
      "inner product space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}