Wavelet and Linear Algebra

Abstract
Consider a locally compact group $G$ with two compact subgroups $H$ and $K$. Equip the double coset space $K\setminus G/H$ with the quotient topology. Suppose that $\mu$ is an $N$-relatively invariant measure, on $K\setminus G/H$.
We define a multiplication on $L^1(K\setminus G/H,\mu)$ such that  this space becomes a Banach algebra  that possesses a left (right) approximate identity.