Ideals with bounded approximate identities in the Fourier algebras on homogeneous spaces (Q1928383)

The author studies closed ideals in the Fourier algebra \(A(G/K)\) of an amenable homogeneous space \(G/K\). Among the results, the author characterizes the closed ideals with bounded approximate identities in the Fourier algebras of an amenable homogeneous space, extending a result of [\textit{B. Forrest} et al., Funct. Anal. 203, No. 1, 286--304 (2003; Zbl 1039.46042)]. He also studies \(A_0(G/K)\), the closure of \(A(G/K)\) with respect to the completely bounded multiplier norm, and extends some of his results to the Figà-Talamanca-Herz algebra \(A^p(G/K)\) of the homogeneous space \(G/K\).