**Note room change**
(Postponed from October 5, 2018)
Nico Spronk, Pure Mathematics, University of Waterloo
"On operator amenability of Fourier-Steiltjes algebras"
Let $G$ be a locally compact group. The Fourier and Fourier-Stieltjes algebras, $A(G)$ and $B(G)$ are dual objects to the group and measure algebras $L^1(G)$ and $M(G)$, respectively, in a manner which generalizes Pontryagin duality. It is now classical that $L^1(G)$ is (operator) amenable exactly when $G$ is amenable, exactly when $A(G)$ is operator amenable. $M(G)$ is (operator) amenable exactly when G is discrete and abelian; hence $B(G)$ ought to be operator amenable exactly when $G$ is compact. This is not true, generally; but is true for connected groups.
MC 5479