{
  "id": "0810.5540",
  "version": "v1",
  "published": "2008-10-30T18:59:20.000Z",
  "updated": "2008-10-30T18:59:20.000Z",
  "title": "Uniform approximation on ideals of multilinear mappings",
  "authors": [
    "Geraldo Botelho",
    "Pablo Galindo",
    "Leonardo Pellegrini"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For each ideal of multilinear mappings $\\cal M$ we explicitly construct a corresponding ideal $^{a}{\\cal M}$ such that multilinear forms in $^{a}{\\cal M}$ are exactly those which can be approximated, in the uniform norm, by multilinear forms in ${\\cal M}$. This construction is then applied to finite type, compact, weakly compact and absolutely summing multilinear mappings. It is also proved that the correspondence ${\\cal M} \\mapsto ^{a}{\\cal M}$ is Aron-Berner stability preserving.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-30T18:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G25"
    ],
    "keywords": [
      "uniform approximation",
      "multilinear forms",
      "uniform norm",
      "aron-berner stability",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.5540B"
    }
  }
}