{
  "id": "math/0009034",
  "version": "v1",
  "published": "2000-09-04T09:35:01.000Z",
  "updated": "2000-09-04T09:35:01.000Z",
  "title": "Boundedness and surjectivity in Banach spaces",
  "authors": [
    "Olav Nygaard"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We define the ($w^\\ast$-) boundedness property and the ($w^\\ast$-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called ($w^\\ast$-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of two $w^\\ast$-thick sets in $\\Xastast$ and $\\Yast$ is a $w^\\ast$-thick subset in $L(X,Y)^\\ast$ and obtain as a concequense that the set $w^\\ast -exp\\:B_{K(l_2)^\\ast}$ is $w^\\ast$-thick.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-04T09:35:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "banach spaces",
      "boundedness property",
      "complete normed spaces",
      "surjectivity property",
      "tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9034N"
    }
  }
}