{
  "id": "math/0402202",
  "version": "v1",
  "published": "2004-02-12T14:07:28.000Z",
  "updated": "2004-02-12T14:07:28.000Z",
  "title": "Weakly null sequences in the Banach space C(K)",
  "authors": [
    "I. Gasparis",
    "E. Odell",
    "B. Wahl"
  ],
  "comment": "36 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Banach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c_0, the Banach space of null scalar sequences. As an application of this criterion, it is shown that every normalized weakly null sequence in C(K), for countable K, admits a block basis of normalized averages equivalent to the unit vector basis of c_0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-12T14:07:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03"
    ],
    "keywords": [
      "banach space",
      "unit vector basis",
      "normalized weakly null sequence",
      "normalized averages equivalent",
      "block basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2202G"
    }
  }
}