{
  "id": "1103.5318",
  "version": "v2",
  "published": "2011-03-28T10:19:32.000Z",
  "updated": "2011-03-29T13:04:44.000Z",
  "title": "A geometric form of the Hahn-Banach extension theorem for L0 linear functions and the Goldstine-Weston theorem in random normed modules",
  "authors": [
    "Shien Zhao",
    "Guang Shi"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we present a geometric form of the Hahn-Banach extension theorem for $L^{0}-$linear functions and prove that the geometric form is equivalent to the analytic form of the Hahn-Banach extension theorem. Further, we use the geometric form to give a new proof of a known basic strict separation theorem in random locally convex modules. Finally, using the basic strict separation theorem we establish the Goldstine-Weston theorem in random normed modules under the two kinds of topologies----the $(\\epsilon,\\lambda)-$topology and the locally $L^{0}-$convex topology, and also provide a counterexample showing that the Goldstine-Weston theorem under the locally $L^{0}-$convex topology can only hold for random normed modules with the countable concatenation property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-29T13:04:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A22",
      "46A16",
      "46A16",
      "46H25",
      "46H05"
    ],
    "keywords": [
      "hahn-banach extension theorem",
      "random normed modules",
      "geometric form",
      "goldstine-weston theorem",
      "l0 linear functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.5318Z"
    }
  }
}