{
  "id": "1207.4719",
  "version": "v1",
  "published": "2012-07-19T16:10:31.000Z",
  "updated": "2012-07-19T16:10:31.000Z",
  "title": "Embeddings of Müntz Spaces: Composition Operators",
  "authors": [
    "S. Waleed Noor"
  ],
  "comment": "15 Pages; Integral Equations Operator Theory, Springer, 2012",
  "journal": "Integral Equations Operator Theory, Volume 73, Issue 4, 589-602 (2012)",
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a strictly increasing sequence $\\Lambda=(\\lambda_n)$ of nonegative real numbers, with $\\sum_{n=1}^\\infty \\frac{1}{\\lambda_n}<\\infty$, the M\\\"untz spaces $M_\\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\\lambda_n}$. We discuss how properties of the embedding $M_\\Lambda^2\\subset L^2(\\mu)$, where $\\mu$ is a finite positive Borel measure on the interval $[0,1]$, have immediate consequences for composition operators on $M^2_\\Lambda$. We give criteria for composition operators to be bounded, compact, or to belong to the Schatten--von Neumann ideals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-19T16:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E15",
      "46E20",
      "46E35"
    ],
    "keywords": [
      "composition operators",
      "müntz spaces",
      "schatten-von neumann ideals",
      "finite positive borel measure",
      "immediate consequences"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.4719W"
    }
  }
}