{
  "id": "2406.02714",
  "version": "v1",
  "published": "2024-06-04T18:57:54.000Z",
  "updated": "2024-06-04T18:57:54.000Z",
  "title": "$DW$-compact operators on Banach lattices",
  "authors": [
    "Jin Xi Chen",
    "Jingge Feng"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper is devoted to the study of $DW$-compact operators, that is, those operators which map disjointly weakly compact sets in a Banach lattice onto relatively compact sets. We show that $DW$-compact operators are precisely the operators which are both Dunford-Pettis and $AM$-compact. As an application, Banach lattices with the property that every disjointly weakly compact set is a limited (resp. Dunford-Pettis) set, are characterized by using $DW$-compact operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-04T18:57:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42",
      "46B50",
      "47B65"
    ],
    "keywords": [
      "compact operators",
      "banach lattice",
      "map disjointly weakly compact sets",
      "relatively compact sets",
      "dunford-pettis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}