{
  "id": "2006.13021",
  "version": "v1",
  "published": "2020-06-20T19:19:24.000Z",
  "updated": "2020-06-20T19:19:24.000Z",
  "title": "Geometric Properties of some Banach Algebras related to the Fourier algebra on Locally Compact Groups",
  "authors": [
    "Edmond Granirer"
  ],
  "comment": "10 pages. arXiv admin note: substantial text overlap with arXiv:1703.08253",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $A_p(G)$ denote the Figa-Talamanca-Herz Banach Algebra of the locally compact group}} $G$, thus $A_2(G)$ {\\it{is the Fourier Algebra of $G$. If $G$ is commutative then $A_2(G)=L^1(\\hat{G})^\\wedge$. Let $A_p^r(G)=A_p\\cap L^r(G)$ with norm $\\|u\\|_{A_p^r}=\\| u\\|_{A_p}+\\| u\\|_{L^r}$.We investigate for which $p$, $r$, and $G$ do the Banach algebras $A_p^r(G)$ {\\it{have the Banach space geometric properties: The Radon-Nikodym Property (RNP), the Schur Property (SP) or the Dunford-Pettis Property (DPP). The results are new even if $G=R$ (the real line) or $G=Z$ (the additive integers).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-20T19:19:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact group",
      "fourier algebra",
      "banach space geometric properties",
      "figa-talamanca-herz banach algebra",
      "radon-nikodym property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}