Conditions implying the uniqueness of the weak *-topology on certain group algebras

• Autores: Matthew Daws, Hungq Le Pham, Stuart A. White
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 253-276
• Idioma: inglés
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• Resumen

  • We investigate possible preduals of the measure algebra M(G) of a locally compact group and the Fourier algebra A(G) of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak*-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals C0(G) of M(G) and C*(G) of A(G) are uniquely determined. In both cases we consider a natural comultiplication and show that the canonical predual gives rise to the unique weak*-topology making both the multiplication separately weak*-continuous and the comultiplication weak*-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure.