{
  "id": "2207.04972",
  "version": "v1",
  "published": "2022-07-11T15:54:06.000Z",
  "updated": "2022-07-11T15:54:06.000Z",
  "title": "Duals and pullbacks of normed modules",
  "authors": [
    "Nicola Gigli",
    "Danka Lučić",
    "Enrico Pasqualetto"
  ],
  "comment": "35 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of the Lebesgue-Bochner space $L^p([0,1],B)$ consists - quite roughly said - of $L^q$ maps from $[0,1]$ to the dual $B'$ of $B$ equipped with the weak$^*$ topology. In order to state our result, we study various fiberwise descriptions of a normed module that are of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-11T15:54:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18F15",
      "53C23",
      "28A51",
      "46G15"
    ],
    "keywords": [
      "normed module",
      "independent interest",
      "natural generalization",
      "well-known fact",
      "general description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}