Bounded projections on Fourier-Stieltjes transforms

Abstract:

We study certain algebraic projections on the measure algebra (of a locally compact abelian group) which extend to bounded projections on the uniform closure of the Fourier-Stieltjes transforms. These projections arise by studying a Raikov system of subsets induced by locally compact subgroups. These results generalize the inequality $||{\hat \mu _d}|{|_\infty } \leqq ||\hat \mu |{|_\infty }$ (where $\mu$ is in the measure algebra, ${\mu _d}$ is the discrete part of $\mu$, and $||\hat \mu |{|_\infty }$ is the sup-norm of the Fourier-Stieltjes transform).