{
  "id": "1809.03013",
  "version": "v1",
  "published": "2018-09-09T17:36:02.000Z",
  "updated": "2018-09-09T17:36:02.000Z",
  "title": "Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases",
  "authors": [
    "Fernando Albiac",
    "Jose L. Ansorena",
    "Stephen J. Dilworth",
    "Denka Kutzarova"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non superreflexive mixed-norm sequence space. As a by-product of our work, we give applications of this result to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-09T17:36:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B45",
      "46B25",
      "46B15",
      "46B10",
      "46B07",
      "41A65"
    ],
    "keywords": [
      "garling sequence spaces",
      "special types",
      "conditional bases",
      "applications",
      "non-superreflexivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}