{
  "id": "2103.04929",
  "version": "v1",
  "published": "2021-03-08T17:43:00.000Z",
  "updated": "2021-03-08T17:43:00.000Z",
  "title": "Banach Convolution Modules of Group Algebras on Covariant Functions of Characters of Normal Subgroups",
  "authors": [
    "Arash Ghaani Farashahi"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2102.08901",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper investigates structure of Banach convolution modules induced by group algebras on covariant functions of characters of closed normal subgroups. Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a closed normal subgroup of $G$. Suppose that $\\xi:N\\to\\mathbb{T}$ is a continuous character, $1\\le p<\\infty$ and $L_\\xi^p(G,N)$ is the $L^p$-space of all covariant functions of $\\xi$ on $G$. It is shown that $L^p_\\xi(G,N)$ is a Banach $L^1(G)$-module. We then study convolution module actions of group algebras on covariant functions of characters for the case of canonical normal subgroups in semi-direct product groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-08T17:43:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "43A20",
      "43A85"
    ],
    "keywords": [
      "banach convolution modules",
      "covariant functions",
      "group algebra",
      "closed normal subgroup",
      "study convolution module actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}