{
  "id": "1906.02372",
  "version": "v1",
  "published": "2019-06-06T01:17:20.000Z",
  "updated": "2019-06-06T01:17:20.000Z",
  "title": "The forward and backward shift on the Lipschitz space of a tree",
  "authors": [
    "Emmanuel Rivera-Guasco",
    "Rubén A. Martínez-Avendaño"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We initiate the study of the forward and backward shifts on the Lipschitz space of a tree, $\\mathcal L$, and on the little Lipshitz space of a tree, ${\\mathcal L}_0$. We determine that the forward shift is bounded both on $\\mathcal L$ and on ${\\mathcal L}_0$ and, when the tree is leafless, it is an isometry; we also calculate its spectrum. For the backward shift, we determine when it is bounded on $\\mathcal L$ and on ${\\mathcal L}_0$, we find the norm when the tree is homogeneous, we calculate the spectrum for the case when the tree is homogeneous, and we determine, for a general tree, when it is hypercyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-06T01:17:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "47B37",
      "05C05",
      "05C63"
    ],
    "keywords": [
      "backward shift",
      "lipschitz space",
      "little lipshitz space",
      "general tree",
      "forward shift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}