{
  "id": "1709.01114",
  "version": "v1",
  "published": "2017-09-04T18:50:10.000Z",
  "updated": "2017-09-04T18:50:10.000Z",
  "title": "When does $C(K,X)$ contain a complemented copy of $c_0(Γ)$ iff $X$ does?",
  "authors": [
    "Elói Medina Galego",
    "Vinícius Morelli Cortes"
  ],
  "comment": "12 pages, submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $K$ be a compact Hausdorff space with weight w$(K)$, $\\tau$ an infinite cardinal with cofinality cf$(\\tau)$ and $X$ a Banach space. In contrast with a classical theorem of Cembranos and Freniche it is shown that if cf$(\\tau)>$ w$(K)$ then the space $C(K, X)$ contains a complemented copy of $c_{0}(\\tau)$ if and only if $X$ does. This result is optimal for every infinite cardinal $\\tau$, in the sense that it can not be improved by replacing the inequality cf$(\\tau)>$ w$(K)$ by another weaker than it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-04T18:50:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "46E15",
      "46E40",
      "46B25"
    ],
    "keywords": [
      "complemented copy",
      "infinite cardinal",
      "compact hausdorff space",
      "banach space",
      "classical theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}