{
  "id": "2308.16367",
  "version": "v1",
  "published": "2023-08-30T23:56:34.000Z",
  "updated": "2023-08-30T23:56:34.000Z",
  "title": "Automatic continuity of new generalized derivations",
  "authors": [
    "Amin Hosseini",
    "Choonkil Park"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{A}$ and $\\mathcal{B}$ be two algebras and let $n$ be a positive integer. A linear mapping $D:\\mathcal{A} \\rightarrow \\mathcal{B}$ is called a \\emph{strongly generalized derivation of order $n$} if there exist families of linear mappings $\\{E_k:\\mathcal{A} \\rightarrow \\mathcal{B}\\}_{k = 1}^{n}$, $\\{F_k:\\mathcal{A} \\rightarrow \\mathcal{B}\\}_{k = 1}^{n}$, $\\{G_k:\\mathcal{A} \\rightarrow \\mathcal{B}\\}_{k = 1}^{n}$ and $\\{H_k:\\mathcal{A} \\rightarrow \\mathcal{B}\\}_{k = 1}^{n}$ which satisfy $D(ab) = \\sum_{k = 1}^{n}\\left[E_k(a) F_k(b) + G_k(a)H_k(b)\\right]$ for all $a, b \\in \\mathcal{A}$. The purpose of this article is to study the automatic continuity of such derivations on Banach algebras and $C^{\\ast}$-algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-30T23:56:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B48",
      "47B47",
      "46H40"
    ],
    "keywords": [
      "automatic continuity",
      "generalized derivation",
      "banach algebras",
      "linear mapping"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}