{
  "id": "2107.14690",
  "version": "v1",
  "published": "2021-07-30T15:12:42.000Z",
  "updated": "2021-07-30T15:12:42.000Z",
  "title": "Norm-multiplicative homomorphisms of Beurling algebras",
  "authors": [
    "Matthew E. Kroeker",
    "Alexander Stephens",
    "Ross Stokke",
    "Randy Yee"
  ],
  "comment": "26 pages",
  "categories": [
    "math.FA",
    "math.RA"
  ],
  "abstract": "We introduce and study \"norm-multiplicative\" homomorphisms $\\varphi: {\\cal L}^1(F) \\rightarrow {\\cal M}_r(G)$ between group and measure algebras, and $\\varphi: {\\cal L}^1(\\omega_F) \\rightarrow {\\cal M}(\\omega_G)$ between Beurling group and measure algebras, where $F$ and $G$ are locally compact groups with continuous weights $\\omega_F$ and $\\omega_G$. Through a unified approach we recover, and sometimes strengthen, many of the main known results concerning homomorphisms and isomorphisms between these (Beurling) group and measure algebras. We provide a first description of all positive homomorphisms $\\varphi: {\\cal L}^1(F) \\rightarrow {\\cal M}_r(G)$. We state versions of our results that describe a variety of (possibly unbounded) homomorphisms $\\varphi: \\mathbb{C} F \\rightarrow \\mathbb{C} G$ for (discrete) groups $F$ and $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-30T15:12:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A20",
      "43A10",
      "43A15",
      "43A22",
      "16S34"
    ],
    "keywords": [
      "beurling algebras",
      "norm-multiplicative homomorphisms",
      "measure algebras",
      "locally compact groups",
      "results concerning homomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}