{
  "id": "2207.12645",
  "version": "v1",
  "published": "2022-07-26T04:17:01.000Z",
  "updated": "2022-07-26T04:17:01.000Z",
  "title": "Multiplication operators between Lipschitz-type spaces on a tree",
  "authors": [
    "Robert F. Allen",
    "Flavia Colonna",
    "Glenn R. Easley"
  ],
  "journal": "Int. J. Math. Math. Sci. 2011, Art. ID 472495, 36 pp",
  "doi": "10.1155/2011/472495",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{L}$ be the space of complex-valued functions $f$ on the set of vertices $T$ of an rooted infinite tree rooted at $o$ such that the difference of the values of $f$ at neighboring vertices remains bounded throughout the tree, and let $\\mathcal{L}_{\\textbf{w}}$ be the set of functions $f\\in \\mathcal{L}$ such that $|f(v)-f(v^-)|=O(|v|^{-1})$, where $|v|$ is the distance between $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. In this article, we characterize the bounded and the compact multiplication operators between $\\mathcal{L}$ and $\\mathcal{L}_{\\textbf{w}}$, and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between $\\mathcal{L}_{\\textbf{w}}$ and the space $L^\\infty$ of bounded functions on $T$ and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-26T04:17:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "05C05"
    ],
    "keywords": [
      "lipschitz-type spaces",
      "compact multiplication operators",
      "operator norm",
      "neighboring vertices remains bounded throughout",
      "essential norm estimates"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}