{
  "id": "1912.03402",
  "version": "v1",
  "published": "2019-12-07T00:54:47.000Z",
  "updated": "2019-12-07T00:54:47.000Z",
  "title": "On linear chaos in function spaces",
  "authors": [
    "John M. Jimenez",
    "Marat V. Markin"
  ],
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "We show that, in $L_{p}(0,\\infty)$ $(1\\leq p <\\infty)$, the bounded weighted backward shift operator $(Tx)(t)=wx(t+a)$ ($w>1$ and $a>0$) and its unbounded counterpart $(Tx)(t)=w^{t}x(t+a)$ are chaotic. We also extend the unbounded case to the space $C_{0}[0,\\infty)$ and analyze the spectral structure of the above operators provided the corresponding spaces are complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-07T00:54:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "47A10"
    ],
    "keywords": [
      "function spaces",
      "linear chaos",
      "bounded weighted backward shift operator",
      "spectral structure",
      "unbounded counterpart"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}