F. Fahimian - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box ۱۱۵۹-۹۱۷۷۵, Mashhad, Islamic Republic of Iran.
R. A. Kamyabi-Gol - Department of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS) Islamic Republic of Iran.
F. Esmaeelzadeh - Department of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Islamic Republic of Iran.

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^۱(K\setminus G/H,\mu) such that  this space becomes a Banach algebra  that possesses a left (right) approximate identity.