The Representations and Positive Type Functions of Some Homogenous Spaces
Author(s):
Abstract:
ýFor a homogeneous spaces ý$ýG/Hý$ý, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ý$ýGý$ý. ýAlso we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of $G/H$ý. We propose a relation between cyclic representations of $L^1(G/H)$ and positive type functions on $G/H$ý. We prove that the Gelfand Raikov theorem for $G/H$ holds if and only if $H$ is normalý.
Keywords:
Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:11 Issue: 1, May 2016
Pages:
47 to 56
https://www.magiran.com/p1527385