{
  "id": "math/0002241",
  "version": "v1",
  "published": "2000-02-28T19:02:34.000Z",
  "updated": "2000-02-28T19:02:34.000Z",
  "title": "Complemented subspaces of locally convex direct sums of Banach spaces",
  "authors": [
    "Alex Chigogidze"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that a complemented subspace of a locally convex direct sum of an uncountable collection of Banach spaces is a locally convex direct sum of complemented subspaces of countable subsums. As a corollary we prove that a complemented subspace of a locally convex direct sum of arbitrary collection of $\\ell_{1}(\\Gamma)$-spaces is isomorphic to a locally convex direct sum of $\\ell_{1}(\\Gamma)$-spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-28T19:02:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M10",
      "46B25"
    ],
    "keywords": [
      "locally convex direct sum",
      "complemented subspace",
      "banach spaces",
      "arbitrary collection",
      "uncountable collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2241C"
    }
  }
}