{
  "id": "math/0608087",
  "version": "v2",
  "published": "2006-08-03T11:59:29.000Z",
  "updated": "2006-10-17T11:42:14.000Z",
  "title": "Closed graph and open mapping theorems for topological $\\wt{\\C}$-modules and applications",
  "authors": [
    "Claudia Garetto"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We present closed graph and open mapping theorems for $\\wt{\\C}$-linear maps acting between suitable classes of topological and locally convex topological $\\wt{\\C}$-modules. This is done by adaptation of De Wilde's theory of webbed spaces and Adasch's theory of barrelled spaces to the context of locally convex and topological $\\wt{\\C}$-modules respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach $\\wt{\\C}$-modules. In particular we obtain a necessary condition for $\\Ginf$-hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-17T11:42:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13J99",
      "46A30",
      "46F30"
    ],
    "keywords": [
      "open mapping theorems",
      "closed graph",
      "topological",
      "applications",
      "locally convex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8087G"
    }
  }
}