{
  "id": "1501.07245",
  "version": "v1",
  "published": "2015-01-28T19:13:55.000Z",
  "updated": "2015-01-28T19:13:55.000Z",
  "title": "Approximate indicators for closed subgroups of locally compact groups with applications to weakly amenable groups",
  "authors": [
    "Zsolt Tanko"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We generalize the notion of an approximate indicator for a closed subgroup $H$ of a locally compact group $G$ introduced by Aristov, Runde, and Spronk and extend their characterization of the existence of such nets in terms of the approximability of $\\chi_{H}$ in an appropriate ${weak}^{*}$ topology. We find that this equivalent condition is satisfied whenever $H$ is weakly amenable and $\\chi_{H}$, considered as acting on $\\ell^{1}(G)$ by multiplication, extends to a bounded map on $VN(G)$. This occurs in particular when a natural projection $VN(G)arrow I(A(G),H)^{\\perp}$ exists. Applications are obtained to the existence (and non-existence) of natural and invariant projections onto $I(A(G),H)^{\\perp}$ and $I(A_{cb}(G),H)^{\\perp}$ and to the existence of ($\\Delta$-weak) bounded approximate identities in ideals of $A(G)$ and $A_{cb}(G)$. In particular, we exhibit a locally compact group without the invariant complementation property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-28T19:13:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A22",
      "46J10",
      "46L07"
    ],
    "keywords": [
      "locally compact group",
      "weakly amenable groups",
      "approximate indicator",
      "closed subgroup",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150107245T"
    }
  }
}