{
  "id": "math/0210228",
  "version": "v1",
  "published": "2002-10-15T21:01:06.000Z",
  "updated": "2002-10-15T21:01:06.000Z",
  "title": "Complemented Subspaces of L_p Determined by Partitions and Weights",
  "authors": [
    "Dale Alspach",
    "Simei Tong"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well-known complemented subspaces of L_p. It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions and weights to be isomorphic to a subspace of L_p. Using this we define a space Y_n with norm given by partitions and weights with distance to any subspace of L_p growing with n. This allows us to construct an example of a Banach space with norm given by partitions and weights which is not isomorphic to a subspace of L_p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-15T21:01:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46E30"
    ],
    "keywords": [
      "partitions",
      "banach sequence space",
      "systematic approach",
      "banach space",
      "well-known complemented subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10228A"
    }
  }
}