{
  "id": "1209.1461",
  "version": "v1",
  "published": "2012-09-07T08:37:56.000Z",
  "updated": "2012-09-07T08:37:56.000Z",
  "title": "On similarity of quasinilpotent operators",
  "authors": [
    "Stanislav Shkarin"
  ],
  "journal": "J. Funct. Anal. 241 (2006), 528-556",
  "categories": [
    "math.FA"
  ],
  "abstract": "Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of $C[0,1]$, which answers a question raised by Armando Villena. A sufficient condition for an injective bounded linear operator on a Banach space to determine its topology is obtained. From this condition it follows, for instance, that the Volterra operator acting on the Hardy space $\\H^p$ of the unit disk determines the topology of $\\H^p$ for any $p\\in[1,\\infty]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-07T08:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "46H40"
    ],
    "keywords": [
      "quasinilpotent operators",
      "similarity",
      "volterra operator",
      "unit disk determines",
      "separable banach spaces algebraically similar"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}