{
  "id": "1504.06862",
  "version": "v1",
  "published": "2015-04-26T18:34:41.000Z",
  "updated": "2015-04-26T18:34:41.000Z",
  "title": "Amalgamations of classes of Banach spaces with a monotone basis",
  "authors": [
    "Ondřej Kurka"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It was proved by Argyros and Dodos that, for many classes $ C $ of separable Banach spaces which share some property $ P $, there exists an isomorphically universal space that satisfies $ P $ as well. We introduce a variant of their amalgamation technique which provides an isometrically universal space in the case that $ C $ consists of spaces with a monotone Schauder basis. For example, we prove that if $ C $ is a set of separable Banach spaces which is analytic with respect to the Effros-Borel structure and every $ X \\in C $ is reflexive and has a monotone Schauder basis, then there exists a separable reflexive Banach space that is isometrically universal for $ C $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-26T18:34:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "54H05",
      "46B15",
      "46B20",
      "46B70"
    ],
    "keywords": [
      "monotone basis",
      "monotone schauder basis",
      "separable banach spaces",
      "isomorphically universal space",
      "isometrically universal space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406862K"
    }
  }
}