{
  "id": "math/0607730",
  "version": "v1",
  "published": "2006-07-28T05:45:24.000Z",
  "updated": "2006-07-28T05:45:24.000Z",
  "title": "Basic topological and geometric properties of Cesàro--Orlicz spaces",
  "authors": [
    "Yunan Cui",
    "Henryk Hudzik",
    "Narin Petrot",
    "Suthep Suantai",
    "Alicja Szymaszkiewicz"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Necessary and sufficient conditions under which the Ces\\`{a}ro--Orlicz sequence space $\\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Ces\\`{a}ro--Orlicz spaces $\\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\\cfi$ are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-28T05:45:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B45",
      "46E30"
    ],
    "keywords": [
      "geometric properties",
      "cesàro-orlicz spaces",
      "basic topological",
      "strict convexity",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7730C"
    }
  }
}