{
  "id": "1706.00701",
  "version": "v1",
  "published": "2017-06-02T14:40:38.000Z",
  "updated": "2017-06-02T14:40:38.000Z",
  "title": "Homomorphisms with small bound between Fourier algebras",
  "authors": [
    "Yulia Kuznetsova",
    "Jean Roydor"
  ],
  "journal": "Israel Journal of Mathematics Isreal J. Math. 217 (2017), Iss. 1, pp. 283-301",
  "categories": [
    "math.FA"
  ],
  "abstract": "Inspired by Kalton and Wood's work on group algebras, we describe almost completely contractive algebra homomorphisms from Fourier algebras into Fourier-Stieltjes algebras (endowed with their canonical operator space structure). We also prove that two locally compact groups are isomorphic if and only if there exists an algebra isomorphism $T$ between the associated Fourier algebras (resp. Fourier-Stieltjes algebras) with completely bounded norm $\\| T \\|_{cb} < \\sqrt {3/2}$ (resp. $ \\| T \\|_{cb} < \\sqrt {5}/2$). We show similar results involving the norm distortion $\\| T \\| \\| T ^{-1} \\|$ with universal but non-explicit bound. Our results subsume Walter's well-known structural theorems and also Lau's theorem on second conjugate of Fourier algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-02T14:40:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "46L10",
      "46L07",
      "46L25"
    ],
    "keywords": [
      "fourier algebras",
      "small bound",
      "subsume walters well-known structural theorems",
      "homomorphisms",
      "results subsume walters well-known structural"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}