{
  "id": "1909.04874",
  "version": "v1",
  "published": "2019-09-11T06:57:22.000Z",
  "updated": "2019-09-11T06:57:22.000Z",
  "title": "Approximate semi-amenability of Banach algebras",
  "authors": [
    "M. Shams Kojanaghi",
    "K. Haghnejad Azar",
    "M. R. Mardanbeigi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathfrak{A}$ be a Banach algebra, and $\\mathcal{X}$ a Banach $\\mathfrak{A}$-bimodule. A bounded linear mapping $\\mathcal{D}:\\mathfrak{A}\\rightarrow \\mathcal{X}$ is approximately semi-inner derivation if there eixist nets $(\\xi_{\\alpha})_{\\alpha}$ and $(\\mu_{\\alpha})_{\\alpha}$ in $\\mathcal{X}$ suh that, for each $a\\in\\mathfrak{A}$, $\\mathcal{D}(a)=\\lim_{\\alpha}(a.\\xi_{\\alpha}-\\mu_{\\alpha}.a)$. $\\mathfrak{A}$ is called approximately semi-amenable if for every Banach $\\mathfrak{A}$-bimodule $\\mathcal{X}$, every $\\mathcal{D}\\in\\mathcal{Z}^{1}(\\mathfrak{A},\\mathcal{X}^{*})$ is approximtely semi-inner. There are some Banach algebras which are approximately semi-amenable, but not approximately amenable. In this manuscript, we investigate some properties of approximate semi-amenability of Banach algebras. Also in Theorem \\ref{ee} we prove the approximate semi-amenability of Segal algebras on a locally compact, SIN group $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-11T06:57:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach algebra",
      "approximate semi-amenability",
      "sin group",
      "segal algebras",
      "eixist nets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}