Invariant Subsets and Homological Properties of Orlicz Modules over Group Algebras

Abstract

Let G be a locally compact group with left Haar measure. We study the closed convex left invariant subsets of L-Phi(G) and characterize affine mappings from the space of nonnegative functions in L-1(G) of norm 1 into L-Phi(G) spaces. We apply the results to the study of the multipliers of L-Phi(G). We also investigate the homological properties of L-Phi(G) as a Banach left L-1(G)-module such as projectivity, injectivity and flatness.