{
  "id": "1507.03241",
  "version": "v1",
  "published": "2015-07-12T15:28:20.000Z",
  "updated": "2015-07-12T15:28:20.000Z",
  "title": "Closed ideals in $\\mathcal{L}(X)$ and $\\mathcal{L}(X^*)$ when $X$ contains certain copies of $\\ell_p$ and $c_0$",
  "authors": [
    "Ben Wallis"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Suppose $X$ is a real or complexified Banach space containing a complemented copy of $\\ell_p$, $p\\in(1,2)$, and a copy (not necessarily complemented) of either $\\ell_q$, $q\\in(p,\\infty)$, or $c_0$. Then $\\mathcal{L}(X)$ and $\\mathcal{L}(X^*)$ each admit continuum many closed ideals. If in addition $q\\geq p'$, $\\frac{1}{p}+\\frac{1}{p'}=1$, then the closed ideals of $\\mathcal{L}(X)$ and $\\mathcal{L}(X^*)$ each fail to be linearly ordered. We obtain additional results in the special cases of $\\mathcal{L}(\\ell_1\\oplus\\ell_q)$ and $\\mathcal{L}(\\ell_p\\oplus c_0)$, $1<p<2<q<\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-12T15:28:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "closed ideals",
      "admit continuum",
      "additional results",
      "special cases",
      "complexified banach space containing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703241W"
    }
  }
}