{
  "id": "2304.12042",
  "version": "v1",
  "published": "2023-04-24T12:38:08.000Z",
  "updated": "2023-04-24T12:38:08.000Z",
  "title": "On the constant of Lipschitz approximability",
  "authors": [
    "Rubén Medina"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "In this note we find $\\lambda>1$ and give an explicit construction of a separable Banach space $X$ such that there is no $\\lambda$-Lipschitz retraction from $X$ onto any compact convex subset of $X$ whose closed linear span is $X$. This is closely related to a well-known open problem raised by Godefroy and Ozawa in 2014 and represent the first known example with such a property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-24T12:38:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B80",
      "51F30",
      "54C15"
    ],
    "keywords": [
      "lipschitz approximability",
      "well-known open problem",
      "compact convex subset",
      "explicit construction",
      "separable banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}