{
  "id": "1508.05059",
  "version": "v1",
  "published": "2015-08-20T18:02:51.000Z",
  "updated": "2015-08-20T18:02:51.000Z",
  "title": "Non-universal families of separable Banach spaces",
  "authors": [
    "Ondřej Kurka"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that if $ C $ is a family of separable Banach spaces which is analytic with respect to the Effros-Borel structure and none member of $ C $ is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for $ C $ but still not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-20T18:02:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "54H05",
      "46B15",
      "46B20",
      "46B25"
    ],
    "keywords": [
      "separable banach space",
      "non-universal families",
      "monotone schauder basis",
      "isometrically universal",
      "effros-borel structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805059K"
    }
  }
}