Benjamin Anderson-Sackaney, Department of Pure Mathematics, University of Waterloo
"Fourier-Stieltjes algebras"
In this talk, our goal will be to understand what the Fourier-Stieltjes algebra $B(G)$ is. We will first see the equivalent definitions of $B(G)$. Then we will see some important subspaces of $B(G)$, namely the Fourier algebra and a generalization of this subspace. To conclude, we will look at the functorial properties of $B(G)$ and the celebrated Host's Idempotent. The former studies how continuous group homomorphisms lead to linear contractions between their respective Fourier-Stieltjes algebras and subspaces. The latter characterizes the integer valued functions in $B(G)$ and in particular its idempotents. I will assume basic facts about Banach algebras (specifically $C^*$ algebras and von Neumann algebras), and abelian and compact Harmonic analysis.
MC 5417