{
  "id": "math/9302204",
  "version": "v1",
  "published": "1993-02-02T17:52:31.000Z",
  "updated": "1993-02-02T17:52:31.000Z",
  "title": "The Complete Continuity Property and Finite Dimensional Decompositions",
  "authors": [
    "Maria Girardi",
    "William B. Johnson"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A Banach space $\\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\\X$ is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP (resp., failing the CCP and failing cotype) has a subspace with a finite dimensional decomposition (resp., basis) which fails the CCP.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-02-02T17:52:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite dimensional decomposition",
      "complete continuity property",
      "banach space",
      "maps weakly convergent sequences",
      "norm convergent sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......2204G"
    }
  }
}