{
  "id": "2201.07230",
  "version": "v1",
  "published": "2022-01-18T11:57:29.000Z",
  "updated": "2022-01-18T11:57:29.000Z",
  "title": "On the algebraic structures in $\\A_Φ(G)$",
  "authors": [
    "Ibrahim Akbaroglu",
    "Hasan P. Aghababa",
    "Hamid Rahkooy"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $G$ be a locally compact group and $(\\Phi, \\Psi)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Fig\\`a-Talamanca-Herz-Orlicz algebra ${\\A}_{\\Phi}(G)$ is a Banach algebra under convolution product if and only if $G$ is compact. Then it is shown that ${\\A}_{\\Phi}(G)$ is a Segal algebra, and as a consequence, the amenability of ${\\A}_{\\Phi}(G)$ and the existence of a bounded approximate identity for ${\\A}_{\\Phi}(G)$ under the convolution product is discussed. Furthermore, it is shown that for a compact abelian group $G$, the character space of ${\\A}_{\\Phi}(G)$ under convolution product can be identified with $\\widehat{G}$, the dual of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-18T11:57:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "46E30",
      "54E52"
    ],
    "keywords": [
      "algebraic structures",
      "convolution product",
      "compact abelian group",
      "segal algebra",
      "character space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}