{
  "id": "1705.04635",
  "version": "v1",
  "published": "2017-05-12T15:49:28.000Z",
  "updated": "2017-05-12T15:49:28.000Z",
  "title": "Local approach to order continuity in Cesàro function spaces",
  "authors": [
    "Tomasz Kiwerski",
    "Jakub Tomaszewski"
  ],
  "comment": "18 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The goal of this paper is to present a complete characterisation of points of order continuity in abstract Ces\\`aro function spaces $CX$ for $X$ being a symmetric function space. Under some additional assumptions mentioned result takes the form $(CX)_a = C(X_a)$. We also find simple equivalent condition for this equality which in the case of $I=[0,1]$ comes to $X\\neq L^\\infty$. Furthermore, we prove that $X$ is order continuous if and only if $CX$ is, under assumption that the Ces\\`aro operator is bounded on $X$. This result is applied to particular spaces, namely: Ces\\`aro-Orlicz function spaces, Ces\\`aro-Lorentz function spaces and Ces\\`aro-Marcinkiewicz function spaces to get criteria for OC-points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-12T15:49:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cesàro function spaces",
      "order continuity",
      "local approach",
      "symmetric function space",
      "additional assumptions mentioned result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}