{
  "id": "2010.06650",
  "version": "v1",
  "published": "2020-10-13T19:35:32.000Z",
  "updated": "2020-10-13T19:35:32.000Z",
  "title": "Homomorphisms of Fourier-Stieltjes algebras",
  "authors": [
    "Ross Stokke"
  ],
  "comment": "40 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Every homomorphism $\\varphi: B(G) \\rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $\\alpha: Y \\rightarrow \\Delta(B(G))$, where $Y$ is a set in the open coset ring of $H$ and $\\Delta(B(G))$ is the Gelfand spectrum of $B(G)$ (a $*$-semigroup). We exhibit a large collection of maps $\\alpha$ for which $\\varphi=j_\\alpha: B(G) \\rightarrow B(H)$ is a completely positive/completely contractive/completely bounded homomorphism and establish converse statements in several instances. For example, we fully characterize all completely positive/completely contractive/completely bounded homomorphisms $\\varphi: B(G) \\rightarrow B(H)$ when $G$ is a Euclidean- or $p$-adic-motion group. In these cases, our description of the completely positive/completely contractive homomorphisms employs the notion of a \"fusion map of a compatible system of homomorphisms/affine maps\" and is quite different from the Fourier algebra situation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-13T19:35:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A30",
      "43A22",
      "43A70",
      "47L25"
    ],
    "keywords": [
      "fourier-stieltjes algebras",
      "positive/completely contractive/completely bounded homomorphism",
      "fourier algebra situation",
      "positive/completely contractive homomorphisms employs",
      "establish converse statements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}