In this paper, we suppose that H is a compact subgroup of locally compact topologicalgroup G and G/H is a homogeneous space which is equipped with a strongly quasi-invariant Radon measure µ.Then in the group algebra L1(G), we replace the homogeneousespace G/H in stead of G and consider the new Banach algebra L1(G/H). We study thisBanach algebra and it’s dual. At the end, by characterization of L∞(G/H) and the leftand right dual L1(G/H)-module actions of L∞(G/H), we give a necessary and sufficientconditions for amenability and weak amenability of this Banach algebra
