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

Daws, M., lePham, H. and White, S. (2009) Conditions implying the uniqueness of the weak*-topology on certain group algebras. Houston Journal of Mathematics, 35(1), pp. 253-276.

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: Daws, M., lePham, H., and White, S.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Houston Journal of Mathematics
Journal Abbr.:Houston J. Math.
Publisher:University of Houston
Copyright Holders:Copyright © 2009 University of Houston
First Published:First published in Houston Journal of Mathematics 35(1):253-276
Publisher Policy:Reproduced with permission of the publisher

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