Resumen de Characterizations of Riesz sets

Ali Ulger

• Let G be a compact abelian group, M(G) its measure algebra and L1(G) its group algebra. For a subset E of the dual group Gˆ, let ME(G)={μ∈M(G):μˆ=0 on Gˆ∖E} and L1E(G)={a∈L1(G):aˆ=0 on Gˆ∖E}. The set E is said to be a Riesz set if ME(G)=L1E(G). In this paper we present several characterizations of the Riesz sets in terms of Arens multiplication and in terms of the properties of the Gelfand transform Γ:L1E(G)→c0(E).