{
  "id": "1003.5708",
  "version": "v2",
  "published": "2010-03-30T00:34:27.000Z",
  "updated": "2010-09-10T21:37:42.000Z",
  "title": "Direct sums and the Szlenk index",
  "authors": [
    "Philip A. H. Brooker"
  ],
  "comment": "The proof of Proposition~2.4 has changed, with some of the arguments transferred to the proof of an added-in lemma, Lemma~2.8. Changes have been made to the Applications section",
  "journal": "Journal of Functional Analysis 260 (2011) 2222-2246",
  "doi": "10.1016/j.jfa.2010.12.016",
  "categories": [
    "math.FA"
  ],
  "abstract": "For $\\alpha$ an ordinal and $1<p<\\infty$, we determine a necessary and sufficient condition for an $\\ell_p$-direct sum of operators to have Szlenk index not exceeding $\\omega^\\alpha$. It follows from our results that the Szlenk index of an $\\ell_p$-direct sum of operators is determined in a natural way by the behaviour of the $\\epsilon$-Szlenk indices of its summands. Our methods give similar results for $c_0$-direct sums.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-10T21:37:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct sum",
      "szlenk index",
      "natural way",
      "sufficient condition",
      "similar results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5708B"
    }
  }
}