Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Multiplication on double coset space $L^1(K\setminus G/H)$Multiplication on double coset space $L^1(K\setminus G/H)$37464668610.22072/wala.2020.119154.1262ENF.FahimianDepartment of Pure Mathematics, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Islamic Republic of Iran.R. A.Kamyabi-GolDepartment of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS) Islamic Republic of Iran.F.EsmaeelzadehDepartment of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Islamic Republic of Iran.Journal Article20191225<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_9f07065f47167dcc4da0c9c61eb55d1b.pdf