{
  "id": "0806.4643",
  "version": "v2",
  "published": "2008-06-28T02:31:57.000Z",
  "updated": "2008-11-14T16:59:40.000Z",
  "title": "Norm one idempotent cb-multipliers with applications to the Fourier algebra in the cb-multiplier norm",
  "authors": [
    "Brian E. Forrest",
    "Volker Runde"
  ],
  "comment": "12 pages; minor revisions",
  "journal": "Canadian Math. Bull. 54 (2011), 654-662",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely bounded multipliers of $A(G)$, and let $A_{Mcb}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \\subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{Mcb}(G)$ with an approximate identity bounded by 1, and we characterize those $G$ for which $A_{Mcb}(G)$ is 1-amenable in the sense of B. E. Johnson. (We can even slightly relax the norm bounds.)",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-14T16:59:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A22",
      "20E05",
      "43A30",
      "46J10",
      "46J40",
      "46L07",
      "47L25"
    ],
    "keywords": [
      "fourier algebra",
      "idempotent cb-multipliers",
      "cb-multiplier norm",
      "applications",
      "locally compact group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4643F"
    }
  }
}