{
  "id": "1606.04874",
  "version": "v1",
  "published": "2016-06-15T17:32:45.000Z",
  "updated": "2016-06-15T17:32:45.000Z",
  "title": "On certain product of Banach modules",
  "authors": [
    "Mohammad Ramezanpour"
  ],
  "comment": "4 pages, The 4th Seminar on Functional Analysis and its Applications, 2 March 2016, Ferdowsi University of Mashhad, Iran",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\\ell^1-$direct sum $A\\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\\cdot b_2+b_1\\cdot a_2+b_1b_2),~~ (a_1, a_2\\in A, b_1, b_2\\in B)$$ is a Banach algebra denoted by $A\\bowtie B$. Module extension algebras, Lau product and also the direct sum of Banach algebras are the main examples satisfying this framework. We obtain characterizations of bounded approximate identities, spectrum, and topological center of this product. This provides a unified approach for obtaining some known results of both module extensions and Lau product of Banach algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-15T17:32:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H05",
      "46H20",
      "46H25",
      "46H05"
    ],
    "keywords": [
      "banach modules",
      "banach algebra",
      "direct sum",
      "lau product",
      "module extension algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}