{
  "id": "0708.4195",
  "version": "v2",
  "published": "2007-08-30T16:22:54.000Z",
  "updated": "2009-09-17T14:33:14.000Z",
  "title": "Amenability of ultraproducts of Banach algebras",
  "authors": [
    "Matthew Daws"
  ],
  "comment": "Added appendix which contains an errata for Section 5",
  "journal": "Proc. Edinb. Math. Soc. (2) 52 (2009), no. 2, 307--338.",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of $\\mc A$ is Arens regular, and give some evidence that this is if and only if $\\mc A$ is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapower of a dual Banach algebra. We study how tensor products of ultrapowers behave, and apply this to study the question of when every ultrapower of $\\mc A$ is amenable. We provide an abstract characterisation in terms of something like an approximate diagonal, and consider when every ultrapower of a C$^*$-algebra, or a group $L^1$-convolution algebra, is amenable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-17T14:33:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B08",
      "46B28",
      "46H05",
      "43A20"
    ],
    "keywords": [
      "amenability",
      "ultraproducts",
      "dual banach algebra",
      "ultrapowers behave",
      "arens regular"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4195D"
    }
  }
}