Aasaimani Thamizhazhagan, Department of Pure Mathematics, University of Waterloo
"On the invertible elements of Fourier-Stieltjes algebra"
For a locally compact abelian group $G$ with dual group $\hat G$, we can associate two commutative Banach algebras : $M(G)$, the measure algebra of $G$ and $L^1(G)$, the group algebra of $G$ (an ideal in $M(G)$). For a general locally compact group $G$, the analogous roles of these commutative algebras are played by $B(G)$, the Fourier-Stieltjes algebra of $G$ and $A(G)$, the Fourier algebra of $G$ (an ideal in $B(G)$) in a sense which generalizes the Pontraygin duality on abelian groups. In 60's-70's, Joseph Taylor gave a characterization of invertible measures in $M(G)$ for a locally compact abelian group $G$. I will show how we can interpret this characterization in $B(G)$ for a locally compact group $G$ and show some class of groups for which this is possible.
MC 5479