Zero divisors and L^p(G), II

Peter A. Linnell and Michael J. Puls

Let G be a discrete group, let p$\ge$1, and let L^p(G) denote the Banach space {S_{g $\in$ G}a_gg | S_{g $\in$ G}| a_g|^p < $\infty$}. The following problem will be studied: given 0$\ne$a $\in$ $\mathbb {C}$G and 0$\ne$b $\in$ L^p(G), is a*b$\ne$ 0? We will concentrate on the case G is a free abelian or free group.