{
  "id": "2202.08032",
  "version": "v1",
  "published": "2022-02-16T13:01:06.000Z",
  "updated": "2022-02-16T13:01:06.000Z",
  "title": "Schauder basis in Lipschitz free spaces over nets of $\\mathcal{L}_\\infty$-spaces",
  "authors": [
    "Petr Hájek",
    "Rubén Medina"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In the present note we give a construction (based on a retractional argument) of a Schauder basis for the Lipschitz free space $\\mathcal{F}(N)$, over a net $N$ in any separable infinite dimensional $\\mathcal{L}_\\infty$-space $X$. In particular, this yields the first example of an infinite dimensional Banach space $X$ not containing $c_0$ with such a property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T13:01:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B80"
    ],
    "keywords": [
      "lipschitz free space",
      "schauder basis",
      "infinite dimensional banach space",
      "first example",
      "separable infinite dimensional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}