@article {
author = {Kamyabi Gol, R. A. and Fahimian, F. and Esmaeelzadeh, F.},
title = {Some relations between $L^p$-spaces on locally compact group $G$ and double coset $K\setminus G/H$},
journal = {Journal of Linear and Topological Algebra ( JLTA )},
volume = {09},
number = {02},
pages = {149-163},
year = {2020},
publisher = {Central Tehran Branch, Islamic Azad University},
issn = {2252-0201},
eissn = {2345-5934},
doi = {},
abstract = {Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $K\setminus G/H$, which equipped with an $N$-strongly quasi invariant measure $\mu$, for $1\leq p\leq +\infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(K\setminus G/H,\mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate that $L^p(K\setminus G/H, \mu)$ 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.},
keywords = {Double coset space,$L^p(K\setminus G/H,\mu )$,quotient space of $L^p(G)$,duality of $L^p(K/G,\mu)$},
url = {http://jlta.iauctb.ac.ir/article_673999.html},
eprint = {http://jlta.iauctb.ac.ir/article_673999_6dbe7cdc0ee0b504390c0a3c3fd064cb.pdf}
}