{
  "id": "1702.05050",
  "version": "v1",
  "published": "2017-02-16T17:01:18.000Z",
  "updated": "2017-02-16T17:01:18.000Z",
  "title": "On certain geometric properties in Banach spaces of vector-valued functions",
  "authors": [
    "Jan-David Hardtke"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider a certain type of geometric properties of Banach spaces, which includes for instance octahedrality, almost squareness, lushness and the Daugavet property. For this type of properties, we obtain a general reduction theorem, which, roughly speaking, states the following: if the property in question is stable under certain finite absolute sums (for example finite $\\ell^p$-sums), then it is also stable under the formation of corresponding K\\\"othe-Bochner spaces (for example $L^p$-Bochner spaces). From this general theorem, we obtain as corollaries a number of new results as well as some alternative proofs of already known results concerning octahedral and almost square spaces and their relatives, diameter-two-properties, lush spaces and other classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-16T17:01:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46E40"
    ],
    "keywords": [
      "banach spaces",
      "geometric properties",
      "vector-valued functions",
      "general reduction theorem",
      "finite absolute sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}