{
  "id": "1405.5715",
  "version": "v1",
  "published": "2014-05-22T11:27:39.000Z",
  "updated": "2014-05-22T11:27:39.000Z",
  "title": "Uniqueness of the maximal ideal of operators on the $\\ell_p$-sum of $\\ell_\\infty^n\\ (n\\in\\mathbb{N})$ for $1<p<\\infty$",
  "authors": [
    "Tomasz Kania",
    "Niels Jakob Laustsen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_p}$ and $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_1^n\\bigr)_{\\ell_p}$ whenever $p\\in(1,\\infty)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-22T11:27:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniqueness",
      "banach space",
      "conclusion holds true",
      "unique maximal ideal",
      "american mathematical society"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5715K"
    }
  }
}