  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 $G/H$.
