## Abstract

Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra M_{cb}A(G), which is dual to the representation of the measure algebra M(G), on B(L_{2}(G)). The image algebras of M(G) and M _{cb}A(G) in CBσ(B(L_{2}(G))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G, there is a natural completely isometric representation of UCB(Ĝ)ß on B(L_{2}(G)), which can be regarded as a duality result of Neufang's completely isometric representation theorem for LUC(G)ß.

Original language | English (US) |
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Pages (from-to) | 1133-1161 |

Number of pages | 29 |

Journal | Transactions of the American Mathematical Society |

Volume | 360 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2008 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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