{
  "id": "1906.09706",
  "version": "v1",
  "published": "2019-06-24T03:28:57.000Z",
  "updated": "2019-06-24T03:28:57.000Z",
  "title": "On topologically invariant means on a locally compact group and a conjecture of Paterson",
  "authors": [
    "John Hopfensperger"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact amenable group, and $\\kappa$ be the smallest cardinality of a set of compacta covering $G$. Then $G$ has a Folner net of cardinality $\\kappa$. We construct dense subsets of $TIM(G)$ and $TLIM(G)$ -- the topological (two-sided) invariant means and the topological left invariant means -- in terms of this Folner net. As an application, we give an elementary proof that $|TLIM(G)| = |TIM(G)| = 2^{2^\\kappa}$. We also prove a conjecture of Paterson, that $TLIM(G) = TIM(G)$ iff $G$ has precompact conjugacy classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-24T03:28:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact group",
      "topologically invariant means",
      "conjecture",
      "folner net",
      "construct dense subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}