{
  "id": "1309.3862",
  "version": "v1",
  "published": "2013-09-16T08:54:10.000Z",
  "updated": "2013-09-16T08:54:10.000Z",
  "title": "Weak-star point of continuity property and Schauder bases",
  "authors": [
    "Ginés López Pérez",
    "José A. Soler Arias"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we get that a dual space satisfies the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results in \\cite{DF} obtained for the separable case. Also, as a consequence of the above characterization, the following result obtained in \\cite{R1} is deduced: {\\it every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-16T08:54:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuity property",
      "weak-star point",
      "schauder bases",
      "complete subsequence",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3862L"
    }
  }
}