Fourier–Stieltjes transforms over homogeneous spaces of compact groups

This paper presents a unified operator theory approach to the abstract notion of Fourier–Stieltjes transforms for Banach measure algebras over homogeneous spaces of compact groups. Let H be a closed subgroup of the compact group G and G/H be the left coset space associated to the subgroup H in G. Also, let M(G/H) be the Banach measure space consists of all (bounded) complex Radon measures over the compact homogeneous space G/H. We then study theoretical aspects of operator-valued Fourier–Stieltjes transform for the Banach measure algebras M(G/H). We shall also present a uniqueness theorem for the abstract Fourier–Stieltjes transforms.