{
  "id": "2002.01613",
  "version": "v1",
  "published": "2020-02-05T02:51:09.000Z",
  "updated": "2020-02-05T02:51:09.000Z",
  "title": "Relationships between Cyclic and Hypercyclic Operators",
  "authors": [
    "André Augusto",
    "Leonardo Pellegrini"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \\in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be hypercyclic. One open problem is whether there exists a space where the Hypercyclicity Criterion is also a necessary condition. For a number of reasons, the spaces with very-few operators are some natural candidates to be a positive answer to that problem. In this paper, we provide a theorem that establishes some relationships for operators in these spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T02:51:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypercyclic operators",
      "relationships",
      "hypercyclicity criterion",
      "well-known sufficient condition",
      "natural candidates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}