{
  "id": "1703.06760",
  "version": "v1",
  "published": "2017-03-20T14:16:19.000Z",
  "updated": "2017-03-20T14:16:19.000Z",
  "title": "On the reflexivity of $\\mathcal{P}_{w}(^{n}E;F)$",
  "authors": [
    "Sergio Pérez"
  ],
  "comment": "4 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove that if $E$ and $F$ are reflexive Banach spaces and $G$ is a closed linear subspace of the space $\\mathcal{P}_{w}(^{n}E;F)$ of all $n$-homogeneous polynomials from $E$ to $F$ which are weakly continuous on bounded sets, then $G$ is either reflexive or non-isomorphic to a dual space. This result generalizes \\cite[Theorem 2]{FEDER} and gives the solution to a problem posed by Feder \\cite[Problem 1]{FED}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-20T14:16:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B10",
      "46G25"
    ],
    "keywords": [
      "reflexivity",
      "reflexive banach spaces",
      "closed linear subspace",
      "dual space",
      "result generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}