{
  "id": "math/0406477",
  "version": "v2",
  "published": "2004-06-23T15:56:39.000Z",
  "updated": "2004-12-07T15:38:13.000Z",
  "title": "Some equivalence relations which are Borel reducible to isomorphism between separable Banach spaces",
  "authors": [
    "Valentin Ferenczi",
    "Eloi Medina Galego"
  ],
  "comment": "23 pages; 2 figures",
  "categories": [
    "math.FA",
    "math.LO"
  ],
  "abstract": "We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\\ell_p$ and $L_p$, $1 \\leq p <2$. More precisely, we show that the relation $E_{K_{\\sigma}}$ is Borel reducible to isomorphism and complemented biembeddability between subspaces of $c_0$ or $\\ell_p, 1 \\leq p <2$. We show that the relation $E_{K_{\\sigma}} \\otimes =^+$ is Borel reducible to isomorphism, complemented biembeddability, and Lipschitz equivalence between subspaces of $L_p, 1 \\leq p <2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-12-07T15:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "46B03"
    ],
    "keywords": [
      "separable banach spaces",
      "borel reducible",
      "equivalence relations",
      "isomorphism",
      "complemented biembeddability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6477F"
    }
  }
}