{
  "id": "2401.15373",
  "version": "v1",
  "published": "2024-01-27T10:37:24.000Z",
  "updated": "2024-01-27T10:37:24.000Z",
  "title": "Compactness of averaging operators on Banach function spaces",
  "authors": [
    "Katsuhisa Koshino"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be compact. As a corollary, we show that the averaging operators on the Lorentz space $L^{p,q}(X)$ of $X$ is compact if and only if $X$ is bounded, in the case where $X$ is a doubling and Borel-regular metric measure space with some continuity between metric and measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-27T10:37:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B01",
      "46E30"
    ],
    "keywords": [
      "banach function space",
      "averaging operators",
      "compactness",
      "borel metric measure space",
      "borel-regular metric measure space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}