Characterizations of Riesz sets - Ülger, A. (Mathematica Scandinavica, 2011)
Let G be a compact abelian group, M(G) its measure algebra and L^1(G) its group algebra. For a subset E of the dual group G, let M_E(G)={μM(G):μ=0 on G E} and L_E^1(G)={aL^1(G):a=0 on GE}. The set E is said to be a Riesz set if M_E(G)=L_E^1(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 :L_E^1(G)→ c_0(E).