Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 7 1 2020 08 01 Multiplication on double coset space $L^1(K\setminus G/H)$ Multiplication on double coset space $L^1(K\setminus G/H)$ 37 46 46686 10.22072/wala.2020.119154.1262 EN F. Fahimian Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, 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. Journal Article 2019 12 25 <br />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 $K\setminus G/H$. <br />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. https://wala.vru.ac.ir/article_46686_0b54a9f970d7aceab45b6b4e15349fa2.pdf