Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-0201090220200601Some relations between $L^p$-spaces on locally compact group $G$ and double coset $Ksetminus G/H$149163673999ENR. A.Kamyabi GolDepartment of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS), P. O. Box 1159-91775, Mashhad, IranF.FahimianDepartment of Pure Mathematics, Ferdowsi University of Mashhad,
P. O. Box 1159-91775, Mashhad, IranF.EsmaeelzadehDepartment of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, IranJournal Article20200229Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate that $L^p(Ksetminus G/H, mu)$ is isometrically isomorphic to a closed subspace of $L^p(G)$. These assist us to study the structure of the classical Banach space created on a double coset space by those produced on topological space.http://jlta.iauctb.ac.ir/article_673999_6dbe7cdc0ee0b504390c0a3c3fd064cb.pdf