{
  "id": "1603.05573",
  "version": "v1",
  "published": "2016-03-17T17:06:45.000Z",
  "updated": "2016-03-17T17:06:45.000Z",
  "title": "Shellable weakly compact subsets of $C[0,1]$",
  "authors": [
    "J. Lopez-Abad",
    "P. Tradacete"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that for every weakly compact subset $K$ of $C[0,1]$ with finite Cantor-Bendixson rank, there is a reflexive Banach lattice $E$ and an operator $T:E\\rightarrow C[0,1]$ such that $K\\subseteq T(B_E)$. On the other hand, we exhibit an example of a weakly compact set of $C[0,1]$ homeomorphic to $\\omega^\\omega+1$ for which such $T$ and $E$ cannot exist. This answers a question of M. Talagrand in the 80's.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-17T17:06:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50",
      "46B42",
      "47B07"
    ],
    "keywords": [
      "shellable weakly compact subsets",
      "finite cantor-bendixson rank",
      "reflexive banach lattice",
      "weakly compact set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160305573L"
    }
  }
}