{
  "id": "1905.10719",
  "version": "v1",
  "published": "2019-05-26T03:39:07.000Z",
  "updated": "2019-05-26T03:39:07.000Z",
  "title": "Semi-amenability of Banach algebras",
  "authors": [
    "Mostfa Shams Kojanaghi",
    "Kazem Haghnejad Azar"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{A}$ be a Banach algebra, and $\\mathcal{X}$ be a Banach $\\mathcal{A}$-bimodule. A derivation $\\mathcal{D}:\\mathcal{A}\\rightarrow \\mathcal{X}$ from Banach algebra into Banach space is called semi-inner if there are $\\eta , \\xi \\in \\mathcal{X}$ such that $$ \\mathcal{D}(a)=a.\\eta-\\xi.a=\\delta_{\\eta,\\xi}(a), \\;\\;\\;\\;\\; (a\\in \\mathcal{A}).$$ A Banach algebra $\\mathcal{A}$ is semi-amenable (resp. semi-contractible) if, for each Banach $\\mathcal{A}$-bimodule $\\mathcal{X}$, every derivation $\\mathcal{D}$ from $\\mathcal{A}$ into $\\mathcal{X}^{*}$ (resp. into $\\mathcal{X}$) is semi-inner. In this paper, we study some problems in semi-amenability of Banach algebras which have been studied in amenability case. We extend some definitions and concepts for semi-amenability, that is, we introduce approximately semi-amenability, semi-contractibility with solving some problems which former have been studied for amenability case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-26T03:39:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach algebra",
      "amenability case",
      "banach space",
      "derivation",
      "semi-inner"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}