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 ? is a relatively invariant measure on G/H then there is a well-defined convolution on L1(G/H,?) such that the Banach space L1(G/H,?) becomes a Banach algebra. We also find a generalized definition of this convolution for other Lp-spaces. Finally, we show that various types of involutions can be considered on G/H.