{
  "id": "math/0412171",
  "version": "v1",
  "published": "2004-12-08T17:10:10.000Z",
  "updated": "2004-12-08T17:10:10.000Z",
  "title": "Embedding $\\ell_{\\infty}$ into the space of all Operators on Certain Banach Spaces",
  "authors": [
    "G. Androulakis",
    "K. Beanland",
    "S. J. Dilworth",
    "F. Sanacory"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give sufficient conditions on a Banach space $X$ which ensure that $\\ell_{\\infty}$ embeds in $\\mathcal{L}(X)$, the space of all operators on $X$. We say that a basic sequence $(e_n)$ is quasisubsymmetric if for any two increasing sequences $(k_n)$ and $(\\ell_n)$ of positive integers with $k_n \\leq \\ell_n$ for all $n$, we have that $(e_{k_n})$ dominates $(e_{\\ell_n})$. We prove that if a Banach space $X$ has a seminormalized quasisubsymmetric basis then $\\ell_{\\infty}$ embeds in $\\mathcal{L}(X)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-08T17:10:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B28",
      "46B03"
    ],
    "keywords": [
      "banach space",
      "basic sequence",
      "sufficient conditions",
      "seminormalized quasisubsymmetric basis",
      "increasing sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12171A"
    }
  }
}