{
  "id": "math/9201234",
  "version": "v1",
  "published": "1991-10-11T14:49:01.000Z",
  "updated": "1991-10-11T14:49:01.000Z",
  "title": "Analytic Disks in Fibers over the Unit Ball of a Banach Space",
  "authors": [
    "B. J. Cole",
    "T. W. Gamelin",
    "William B. Johnson"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the spectrum of H^infinity (B), the algebra of bounded analytic functions on the unit ball B of an arbitrary infinite dimensional Banach space. Various other embedding theorems are obtained. For instance, if the Banach space is superreflexive, then the unit ball of a Hilbert space of uncountable dimension can be embedded analytically in the fiber over 0 via an embedding which is uniformly bicontinuous with respect to the Gleason metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1991-10-11T14:49:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit ball",
      "analytic disks",
      "arbitrary infinite dimensional banach space",
      "study biorthogonal sequences",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......1234C"
    }
  }
}