{
  "id": "0708.4029",
  "version": "v1",
  "published": "2007-08-29T21:47:56.000Z",
  "updated": "2007-08-29T21:47:56.000Z",
  "title": "Ultrapowers of Banach algebras and modules",
  "authors": [
    "Matthew Daws"
  ],
  "comment": "17 pages",
  "journal": "Glasg. Math. J. 50 (2008), no. 3, 539--555.",
  "categories": [
    "math.FA"
  ],
  "abstract": "The Arens products are the standard way of extending the product from a Banach algebra $\\mc A$ to its bidual $\\mc A''$. Ultrapowers provide another method which is more symmetric, but one that in general will only give a bilinear map, which may not be associative. We show that if $\\mc A$ is Arens regular, then there is at least one way to use an ultrapower to recover the Arens product, a result previously known for C$^*$-algebras. Our main tool is a Principle of Local Reflexivity result for modules and algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-29T21:47:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B07",
      "46B08",
      "46H05",
      "46H25",
      "46L05"
    ],
    "keywords": [
      "banach algebra",
      "ultrapower",
      "arens product",
      "local reflexivity result",
      "main tool"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4029D"
    }
  }
}