{
  "id": "1711.01340",
  "version": "v1",
  "published": "2017-11-03T21:35:10.000Z",
  "updated": "2017-11-03T21:35:10.000Z",
  "title": "Algebras of diagonal operators of the form scalar-plus-compact are Calkin algebras",
  "authors": [
    "Pavlos Motakis",
    "Daniele Puglisi",
    "Andreas Tolias"
  ],
  "comment": "49 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For every Banach space $X$ with a Schauder basis consider the Banach algebra $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$ of all diagonal operators that are of the form $\\lambda I + K$. We prove that $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$ is a Calkin algbra i.e., there exists a Banach space $\\mathcal{Y}_X$ so that the Calkin algebra of $\\mathcal{Y}_X$ is isomorphic as a Banach algebra to $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$. Among other applications of this theorem we obtain that certain hereditarily indecomposable spaces and the James spaces $J_p$ and their duals endowed with natural multiplications are Calkin algebras, that all non-reflexive Banach spaces with unconditional bases are isomorphic as Banach spaces to Calkin algebras, and that sums of reflexive spaces with unconditional bases with certain James-Tsirelson type spaces are isomorphic as Banach spaces to Calkin algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-03T21:35:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "46B25",
      "46B28",
      "46B45"
    ],
    "keywords": [
      "calkin algebra",
      "diagonal operators",
      "form scalar-plus-compact",
      "unconditional bases",
      "banach algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}