{
  "id": "2203.16617",
  "version": "v1",
  "published": "2022-03-30T19:02:05.000Z",
  "updated": "2022-03-30T19:02:05.000Z",
  "title": "Disjoint hypercyclicity, Sidon sets and weakly mixing operators",
  "authors": [
    "Rodrigo Cardeccia"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that a finite set of natural numbers $J$ satisfies that $J\\cup\\{0\\}$ is not Sidon if and only if for any operator $T$, the disjoint hypercyclicity of $\\{T^j:j\\in J\\}$ implies that $T$ is weakly mixing. As an application we show the existence of a non weakly mixing operator $T$ such that $T\\oplus T^2\\ldots \\oplus T^n$ is hypercyclic for every $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-30T19:02:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disjoint hypercyclicity",
      "sidon sets",
      "natural numbers",
      "non weakly mixing operator",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}