1553

Date | 2014-11-28 |
---|---|

Speaker | 이훈희 |

Dept. | 서울대 |

Room | 129-301 |

Time | 10:30-12:00 |

Since the work of Johnson
characterizing amenability of a locally compact group G in terms of Banach
algebra amenability of the convolution algebra L_{1}(G), questions of
characterizing various amenabilities of group related Banach algebras have been
central theme of abstract harmonic analysis. For example, Ruan proved that
operator space amenability of the Fourier algebra A(G) is equivalent to the
amenability of G and Forrest/Runde showed that amenability of A(G) is
equivalent to G being virtually abelian. In this talk we will focus on the weak
amenability problem of Fourier algebras on Lie groups. We show that for a Lie
group G, its Fourier algebra A(G) is weakly amenable if and only if its
connected component of the identity G_{e} is abelian. Our main new idea is to
show that for connected G, weak amenability of A(G) implies that the
anti-diagonal of the product group G \times G, is a set of local synthesis for A(G\times G). We then to show that
this cannot happen if G is non-abelian.

This is a joint work with Jean Ludwig (Metz), Ebrahim
Samei (Saskatchewan) and Nico Spronk (Waterloo).

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