Ideals with bounded approximate identities in the Fourier algebras on homogeneous spaces

In this paper, the closed ideals with bounded approximate identities in the Fourier algebra of an amenable homogeneous space is characterized in terms of the coset ring of the corresponding group. Some of these results are also extended to the case of Figà–Talamanca–Herz algebra. The closure of the Fourier algebra A(G/K) in the cb-multiplier norm is also considered and we prove some results on spectral synthesis. We also derive some results on the ideals with bounded approximate identity.