Projectivity of Lp (G,ω) as a L1(G )-module

Abstract

Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞ . We show that projectivity of Lp (G,ω) as a Banach left L1 (G) -module is table with respect to ω . In fact we prove that Lp (G,ω) is a projective L1 (G) -module if and only if G is compact.