# Multiplication on double coset space $L^1(K\setminus G/H)$

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Islamic Republic of Iran.

2 Department of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS) Islamic Republic of Iran.

3 Department of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Islamic Republic of Iran.

10.22072/wala.2020.119154.1262

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.

Keywords

#### References

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