{
  "id": "1101.2218",
  "version": "v1",
  "published": "2011-01-11T21:40:26.000Z",
  "updated": "2011-01-11T21:40:26.000Z",
  "title": "Null-orbit reflexive operators",
  "authors": [
    "Don Hadwin",
    "Ileana Ionascu",
    "Hassan Yousefi"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We introduce and study the notion of null-orbit reflexivity, which is a slight perturbation of the notion of orbit-reflexivity. Positive results for orbit reflexivity and the recent notion of $\\mathbb{C}$-orbit reflexivity both extend to null-orbit reflexivity. Of the two known examples of operators that are not orbit-reflexive, one is null-orbit reflexive and the other is not. The class of null-orbit reflexive operators includes the classes of hyponormal, algebraic, compact, strictly block-upper (lower) triangular operators, and operators whose spectral radius is not 1. We also prove that every polynomially bounded operator on a Hilbert space is both orbit-reflexive and null-orbit reflexive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-11T21:40:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null-orbit reflexive operators",
      "null-orbit reflexivity",
      "triangular operators",
      "spectral radius",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.2218H"
    }
  }
}