{
  "id": "2411.07710",
  "version": "v1",
  "published": "2024-11-12T10:53:26.000Z",
  "updated": "2024-11-12T10:53:26.000Z",
  "title": "Symmetrized pseudofunction algebras from $L^p$-representations and amenability of locally compact groups",
  "authors": [
    "Emilie Mai Elkiær"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.GR",
    "math.OA"
  ],
  "abstract": "We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and review various characterizations of group amenability connected to the $p$-pseudofunction algebra of Herz and generalize these to the symmetrized setting. Along the way, we describe the Banach space dual of the symmetrized pseudofuntion algebras on $G$ associated with representations on reflexive Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-12T10:53:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact group",
      "symmetrized pseudofunction algebras",
      "representations",
      "complex interpolation theory",
      "banach space dual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}