TY - JOUR
ID - 673999
TI - Some relations between $L^p$-spaces on locally compact group $G$ and double coset $Ksetminus G/H$
JO - Journal of Linear and Topological Algebra ( JLTA )
JA - JLTA
LA - en
SN - 2252-0201
AU - Kamyabi Gol, R. A.
AU - Fahimian, F.
AU - Esmaeelzadeh, F.
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS), P. O. Box 1159-91775, Mashhad, Iran
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad,
P. O. Box 1159-91775, Mashhad, Iran
AD - Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Iran
Y1 - 2020
PY - 2020
VL - 09
IS - 02
SP - 149
EP - 163
KW - Double coset space
KW - $L^p(Ksetminus G/H,mu )$
KW - quotient space of $L^p(G)$
KW - duality of $L^p(K/G,mu)$
DO -
N2 - Let $H$ 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.
UR - http://jlta.iauctb.ac.ir/article_673999.html
L1 - http://jlta.iauctb.ac.ir/article_673999_6dbe7cdc0ee0b504390c0a3c3fd064cb.pdf
ER -