Hun Hee Lee, Seoul National University
“Weak amenability problem of Fourier algebras”
Since the work of Johnson characterizing amenability of a locally compact group G in terms of Banach algebra amenability of the convolution algebra L1(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 focusing on Lie group cases. More precisely, we will 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 Ge is abelian. Our main new idea is to show that for connected Lie group G, weak amenability of A(G) implies that the anti-diagonal of the product group G × G, is a set of local synthesis for A(G × G), which will be shown not to be possible for non-abelian G.
Refreshments will be served in MC 5413 at 3:30 p.m. Everyone is welcome to attend.