{
  "id": "1008.2651",
  "version": "v1",
  "published": "2010-08-16T13:29:33.000Z",
  "updated": "2010-08-16T13:29:33.000Z",
  "title": "Factorization property and Arens regularity",
  "authors": [
    "Kazem Haghnejad Azar"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. For Banach $A-bimodule$ $B$, let $Z_1(A^{**})$, ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$ be the topological centers of second dual of Banach algebra $A$, left module action $\\pi_\\ell:~A\\times B\\rightarrow B$ and right module action $\\pi_r:~B\\times A\\rightarrow B$, respectively. We establish some relationships between them and factorization properties of $A^*$ and $B^*$. We search some necessary and sufficient conditions for factorization of $A^*$, $B$ and $B^*$ with some results in group algebras. We extend the definitions of the left and right multiplier for module actions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-16T13:29:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L06",
      "46L07",
      "46L10",
      "47L25",
      "F.2.2",
      "I.2.7"
    ],
    "keywords": [
      "factorization property",
      "arens regularity properties",
      "right module action",
      "left module action",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2651H"
    }
  }
}