{
  "id": "1910.08299",
  "version": "v1",
  "published": "2019-10-18T08:06:38.000Z",
  "updated": "2019-10-18T08:06:38.000Z",
  "title": "Geometric Characterization of Preduals of Injective Banach Lattices",
  "authors": [
    "A. G. Kusraev",
    "S. S. Kutateladze"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The paper deals with the study of Banach spaces whose duals are injective Banach lattices. Davies in 1967 proved that an ordered Banach space is an $L^1$-predual space if and only if it is a simplex space. In 2007 Duan and Lin proved that a real Banach space is an $L^1$-predual space if and only if its every four-point subset is centerable. We prove the counterparts of these remarkable results for injectives by the new machinery of Boolean valued transfer from $L^1$-spaces to injective Banach lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-18T08:06:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42",
      "46S99"
    ],
    "keywords": [
      "injective banach lattices",
      "geometric characterization",
      "predual space",
      "real banach space",
      "ordered banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}