{
  "id": "2109.03509",
  "version": "v1",
  "published": "2021-09-08T09:08:11.000Z",
  "updated": "2021-09-08T09:08:11.000Z",
  "title": "Representation theorems for normed modules",
  "authors": [
    "Simone Di Marino",
    "Danka Lučić",
    "Enrico Pasqualetto"
  ],
  "comment": "46 pages",
  "categories": [
    "math.FA",
    "math.DG",
    "math.MG"
  ],
  "abstract": "In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise representative of their elements; to prove that each separable normed module can be represented as the space of sections of a measurable Banach bundle. By combining our representation result with Gigli's differential structure, we eventually show that every metric measure space (whose Sobolev space is separable) is associated with a cotangent bundle in a canonical way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-08T09:08:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "28A51",
      "46G15",
      "13C05",
      "18F15",
      "30L05"
    ],
    "keywords": [
      "normed module",
      "representation theorems",
      "extend von neumanns theory",
      "giglis differential structure",
      "metric measure space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}