Characterizations of Riesz sets

• Autores: Ali Ulger
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 2, 2011, págs. 264-278
• Idioma: inglés
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• Resumen

  • 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).