{
  "id": "0904.4102",
  "version": "v1",
  "published": "2009-04-27T07:43:28.000Z",
  "updated": "2009-04-27T07:43:28.000Z",
  "title": "Approximate Identity and Arens Regularity of Some Banach Algebras",
  "authors": [
    "Kazem Haghnejad Azar",
    "Abdolhamid Riazi"
  ],
  "comment": "15 page",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $A$ be a Banach algebra with the second dual $A^{**}$. If $A$ has a bounded approximate identity $(=BAI)$, then $A^{**}$ is unital if and only if $A^{**}$ has a $weak^* bounded approximate $$identity(=W^*BAI)$. If $A$ is Arens regular and $A$ \\noindent has a BAI, then $A^*$ factors on both sides. In this paper we introduce new concepts $LW^*W$ and $RW^*W$- property and we show that under certain conditions if $A$ has $LW^*W$ and $RW^*W$- property, then $A$ is Arens regular and also if $A$ is Arens regular, then $A$ has $LW^*W$ and $RW^*W$- property. We also offer some applications of these new concepts for the special algebras $l^1(G), L^1(G), M(G)$, and $A(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-27T07:43:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L06",
      "46L07",
      "46L10",
      "47L25"
    ],
    "keywords": [
      "banach algebra",
      "arens regularity",
      "second dual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4102H"
    }
  }
}