Banach Convolution Modules of Group Algebras on Covariant Functions of Characters of Normal Subgroups

8 Mar 2021  ·  Arash Ghaani Farashahi ·

This paper investigates structure of Banach convolution modules induced by group algebras on covariant functions of characters of closed normal subgroups. Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a closed normal subgroup of $G$... Suppose that $\xi:N\to\mathbb{T}$ is a continuous character, $1\le p<\infty$ and $L_\xi^p(G,N)$ is the $L^p$-space of all covariant functions of $\xi$ on $G$. It is shown that $L^p_\xi(G,N)$ is a Banach $L^1(G)$-module. We then study convolution module actions of group algebras on covariant functions of characters for the case of canonical normal subgroups in semi-direct product groups. read more

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Functional Analysis 43A15, 43A20, 43A85