Abstract. In this paper, we investigate the structure of the quasi-regular representation of locally compact groups, particularly focusing on the amenability of the homogeneous factor space G/H by analyzing the C∗-algebras generated by the left quasi-regular representation λG/H. Our main result extends Theorem 1 in [1], establishing a connection between the amenability of the homogeneous space G/H and the existence of a nonzero multiplicative linear functional on C∗(λG/H(G)).
