Convolution and Involution on Function Spaces of Homogeneous Spaces

Let G be a locally compact group and also let H be a compact subgroup of G. It is shown that, if mu is a relatively invariant measure on G/H then there is a well-defined convolution on L-1 (G/H, mu) such that the Banach space L-1 (G/H, mu) becomes a Banach algebra. We also find a generalized definition of this convolution for other L-P-spaces. Finally, we show that various types of involutions can be considered on G/H.