{
  "id": "math/0508028",
  "version": "v2",
  "published": "2005-08-01T09:21:00.000Z",
  "updated": "2006-04-22T08:56:12.000Z",
  "title": "Automatic Continuity of $σ$-Derivations on $C^*$-Algebras",
  "authors": [
    "Madjid Mirzavaziri",
    "Mohammad Sal Moslehian"
  ],
  "comment": "8 pages, some minor corrections, to appear in Proc. Amer. Math. Soc",
  "journal": "Proc. Amer. Math. Soc. 134 (2006), no. 11, 3319-3327.",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $A$ be a $C^*$-algebra acting on a Hilbert space $H$, $\\sigma:A\\to B(H)$ be a linear mapping and $d:A\\to B(H)$ be a $\\sigma$-derivation. Generalizing the celebrated theorem of Sakai, we prove that if $\\sigma$ is a continuous $*$-mapping then $d$ is automatically continuous. In addition, we show the converse is true in the sense that if $d$ is a continuous $*-\\sigma$-derivation then there exists a continuous linear mapping $\\Sigma:A\\to B(H)$ such that $d$ is $*-\\Sigma$-derivation. The continuity of the so-called $*-(\\sigma,\\tau)$-derivations is also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-22T08:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L57",
      "46L05",
      "47B47"
    ],
    "keywords": [
      "derivation",
      "automatic continuity",
      "hilbert space",
      "linear mapping"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8028M"
    }
  }
}