{
  "id": "2205.11608",
  "version": "v1",
  "published": "2022-05-23T20:13:09.000Z",
  "updated": "2022-05-23T20:13:09.000Z",
  "title": "On the reflexivity properties of Banach bundles and Banach modules",
  "authors": [
    "Milica Lučić",
    "Enrico Pasqualetto",
    "Ivana Vojnović"
  ],
  "comment": "24 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $\\sigma$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its $L^p$-sections is uniformly convex for every $p\\in(1,\\infty)$. - If the fibers of a bundle are reflexive, then the space of its $L^p$-sections is reflexive. These results generalise the well-known corresponding ones for Lebesgue-Bochner spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-23T20:13:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18F15",
      "53C23"
    ],
    "keywords": [
      "banach modules",
      "reflexivity properties",
      "finite measure space",
      "uniformly convex",
      "separable measurable banach bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}