{
  "id": "math/0505319",
  "version": "v3",
  "published": "2005-05-16T04:15:08.000Z",
  "updated": "2006-11-22T19:51:36.000Z",
  "title": "$σ$-Derivations in Banach Algebras",
  "authors": [
    "M. Mirzavaziri",
    "M. S. Moslehian"
  ],
  "comment": "12 pages",
  "journal": "Bull. Iranian Math. Soc. 32 (2006), no. 1, 65-78",
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "Introducing the notions of (inner) $\\sigma$-derivation, (inner) $\\sigma$-endomorphism and one-parameter group of $\\sigma$-endomorphisms ($\\sigma$-dynamics) on a Banach algebra, we correspond to each $\\sigma$-dynamics a $\\sigma$-derivation named as its $\\sigma$-infinitesimal generator. We show that the $\\sigma$-infinitesimal generator of a $\\sigma$-dynamics of inner $\\sigma$-endomorphisms is an inner $\\sigma$-derivation and deal with the converse. We also establish a nice generalized Leibniz formula and extend the Kleinenckr--Sirokov theorem for $\\sigma$-derivations under certain conditions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-11-22T19:51:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "47B47",
      "16W25"
    ],
    "keywords": [
      "banach algebra",
      "derivation",
      "infinitesimal generator",
      "endomorphism",
      "nice generalized leibniz formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5319M"
    }
  }
}