This is an announcement for the paper "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" by Matthew Daws, Hung Le Pham and Stuart White.
Abstract: 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 $C_0(G)$ of $M(G)$ and $C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a natural coassociative multiplication and show that the canonical predual gives rise to the unique weak$^*$-topology making both the multiplication separately weak$^*$-continuous and the coassociative multiplication weak$^*$-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 43A20, 43A77
Remarks: 21 pages
The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are) stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding postcript file has gzipped size 133kb.
Submitted from: matt.daws@cantab.net
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