{
  "id": "1010.1298",
  "version": "v4",
  "published": "2010-10-06T23:08:41.000Z",
  "updated": "2011-03-09T16:47:01.000Z",
  "title": "A new and simple proof of Schauder's theorem",
  "authors": [
    "Volker Runde"
  ],
  "comment": "More references added",
  "categories": [
    "math.FA"
  ],
  "abstract": "Schauder's theorem asserts that a bounded linear operator between Banach spaces is compact if ad only if its adjoint is. We give a new proof of this result, which is both short and completely elementary in the sense that it does not depend on anything beyond basic functional analysis, i.e., the Hahn--Banach theorem and some of its consequences; in particular, we avoid the Arzela--Ascoli theorem (and any kind of related diagonal argument).",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-03-09T16:47:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple proof",
      "schauders theorem asserts",
      "basic functional analysis",
      "bounded linear operator",
      "hahn-banach theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.1298R"
    }
  }
}