{
  "id": "1601.04283",
  "version": "v1",
  "published": "2016-01-17T12:27:55.000Z",
  "updated": "2016-01-17T12:27:55.000Z",
  "title": "On the Arens regularity of the Herz Algebra",
  "authors": [
    "Heidar Ghaeid Amini",
    "Ali Rejali"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact group, $A_p (G)$ be the Herz algebra of $G$ associated with $1 <p< \\infty$. We show that $A_p (G)$ is Arens regular if and only if $G$ is a discrete group and for each countable subgroup $H$ of $G$, $A_p (H)$ is Arens regular. In the case $G$ is a countable discrete group we investigate the relations between Arens regularity of $A_p (G)$ and the iterated limit condition. We consider the problem of Arens regularity of $l^1 (G)$ as a subspace of $A_p (G)$. A few related results when the unit ball of $(l^1 (G),.,A_p(G))$ is bounded under $\\|.\\|_1$-norm are also determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-17T12:27:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arens regularity",
      "herz algebra",
      "locally compact group",
      "countable discrete group",
      "iterated limit condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160104283G"
    }
  }
}