Module Maps and Invariant Subsets of Banach Modules of Locally Compact Groups

Abstract

For a locally compact group $G$, Lau and Ghaffari provided many results about $G$-invariant subsets of $G$-modules, and the relationship between $G$-module maps, $L^1(G)$-module maps and $M(G)$- module maps. In both papers their results were specified for one module action. In this paper we extend many of their results to arbitrary Banach $G$-modules and $G$-module maps.