{
  "id": "1812.05025",
  "version": "v1",
  "published": "2018-12-12T16:53:55.000Z",
  "updated": "2018-12-12T16:53:55.000Z",
  "title": "Dedekind complete and order continuous Banach $C(K)$-modules",
  "authors": [
    "Arkady Kitover",
    "Mehmet Orhon"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We extend the notions of Dedekind complete and sigma-Dedekind complete Banach lattices to Banach C(K)-modules. As our main result we prove for these modules an analogue of Lozanovsky's well known characterization of Banach lattices with order continuous norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-12T16:53:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H25",
      "46B42"
    ],
    "keywords": [
      "order continuous banach",
      "sigma-dedekind complete banach lattices",
      "main result",
      "order continuous norm",
      "lozanovskys"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}