{
  "id": "0907.3984",
  "version": "v7",
  "published": "2009-07-23T16:16:04.000Z",
  "updated": "2010-03-20T01:49:07.000Z",
  "title": "B(l^p) is never amenable",
  "authors": [
    "Volker Runde"
  ],
  "comment": "13 pages; final touchups",
  "journal": "J. Amer. Math. Soc. 23 (2010), 1175-1185",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We show that, if $E$ is a Banach space with a basis satisfying a certain condition, then the Banach algebra $\\ell^\\infty({\\cal K}(\\ell^2 \\oplus E))$ is not amenable; in particular, this is true for $E = \\ell^p$ with $p \\in (1,\\infty)$. As a consequence, $\\ell^\\infty({\\cal K}(E))$ is not amenable for any infinite-dimensional ${\\cal L}^p$-space. This, in turn, entails the non-amenability of ${\\cal B}(\\ell^p(E))$ for any ${\\cal L}^p$-space $E$, so that, in particular, ${\\cal B}(\\ell^p)$ and ${\\cal B}(L^p[0,1])$ are not amenable.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2010-03-20T01:49:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L10",
      "46B07",
      "46B45",
      "46H20"
    ],
    "keywords": [
      "banach space",
      "banach algebra",
      "non-amenability"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.3984R"
    }
  }
}