{
  "id": "math/0006134",
  "version": "v2",
  "published": "2000-06-19T20:04:01.000Z",
  "updated": "2000-09-20T15:54:23.000Z",
  "title": "An example of an asymptotically Hilbertian space which fails the approximation property",
  "authors": [
    "P. G. Casazza",
    "C. L. Garcia",
    "W. B. Johnson"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is ``almost'' a weak Hilbert space and which can be written as the direct sum of two subspaces all of whose subspaces have the approximation property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-09-20T15:54:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B07"
    ],
    "keywords": [
      "approximation property",
      "asymptotically hilbertian space",
      "banach space",
      "weak hilbert space",
      "direct sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......6134C"
    }
  }
}