{
  "id": "math/9811145",
  "version": "v1",
  "published": "1998-11-24T18:56:31.000Z",
  "updated": "1998-11-24T18:56:31.000Z",
  "title": "Uniqueness of unconditional bases in c_0-products",
  "authors": [
    "Peter G. Casazza",
    "Nigel J. Kalton"
  ],
  "comment": "23 pages; to appear: Studia Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does c_0(X). In particular, we show that for Tsirelson's space T, every unconditional basis of c_0(T) must be equivalent to a subsequence of the canonical basis but c_0(T) still fails to have a unique unconditional basis. We also give some positive results including a simpler proof that c_0(l_1)has a unique unconditional basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-24T18:56:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B15",
      "46B07"
    ],
    "keywords": [
      "unique unconditional basis",
      "unconditional bases",
      "uniqueness",
      "tsirelsons space",
      "simpler proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11145C"
    }
  }
}