{
  "id": "0801.2477",
  "version": "v1",
  "published": "2008-01-16T16:40:31.000Z",
  "updated": "2008-01-16T16:40:31.000Z",
  "title": "Stability and instability of weighted composition operators",
  "authors": [
    "Jesus Araujo",
    "Juan J. Font"
  ],
  "comment": "37 pages, 7 figures. A beamer presentation at http://www.araujo.tk",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\epsilon >0$. A continuous linear operator $T:C(X) \\ra C(Y)$ is said to be {\\em $\\epsilon$-disjointness preserving} if $\\vc (Tf)(Tg)\\vd_{\\infty} \\le \\epsilon$, whenever $f,g\\in C(X)$ satisfy $\\vc f\\vd_{\\infty} =\\vc g\\vd_{\\infty} =1$ and $fg\\equiv 0$. In this paper we address basically two main questions: 1.- How close there must be a weighted composition operator to a given $\\epsilon$-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given $\\epsilon$-disjointness preserving operator? We address these two questions distinguishing among three cases: $X$ infinite, $X$ finite, and $Y$ a singleton ($\\epsilon$-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-16T16:40:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "46J10",
      "47B33"
    ],
    "keywords": [
      "weighted composition operator",
      "disjointness preserving operator",
      "disjointness preserving functionals",
      "sharp stability",
      "main questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2477A"
    }
  }
}