{
  "id": "0912.1912",
  "version": "v1",
  "published": "2009-12-10T03:58:41.000Z",
  "updated": "2009-12-10T03:58:41.000Z",
  "title": "Borel reducibility and Holder($α$) embeddability between Banach spaces",
  "authors": [
    "Longyun Ding"
  ],
  "comment": "29 pages",
  "categories": [
    "math.LO",
    "math.FA"
  ],
  "abstract": "We investigate Borel reducibility between equivalence relations $E(X,p)=X^{\\Bbb N}/\\ell_p(X)$'s where $X$ is a separable Banach space. We show that this reducibility is related to the so called H\\\"older$(\\alpha)$ embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between $E(L_r,p)$'s and $E(c_0,p)$'s for $r,p\\in[1,+\\infty)$. We also answer a problem presented by Kanovei in the affirmative by showing that $C({\\Bbb R}^+)/C_0({\\Bbb R}^+)$ is Borel bireducible to ${\\Bbb R}^{\\Bbb N}/c_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-10T03:58:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "46B20",
      "47H99"
    ],
    "keywords": [
      "borel reducibility",
      "embeddability",
      "separable banach space",
      "equivalence relations",
      "unreducibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1912D"
    }
  }
}