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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weak*-closedness of subspaces
of Fourier-Stieltjes algebras
and weak*-continuity of the restriction map

Authors: M. B. Bekka, E. Kaniuth, A. T. Lau and G. Schlichting
Journal: Trans. Amer. Math. Soc. 350 (1998), 2277-2296
MSC (1991): Primary 22D10, 43A30
MathSciNet review: 1401762
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Abstract: Let $G$ be a locally compact group and $B(G)$ the Fourier-Stieltjes algebra of $G$. We study the problem of how weak*-closedness of some translation invariant subspaces of $B(G)$ is related to the structure of $G$. Moreover, we prove that for a closed subgroup $H$ of $G$, the restriction map from $B(G)$ to $B(H)$ is weak*-continuous only when $H$ is open in $G$.

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Additional Information

M. B. Bekka
Affiliation: Département de Mathématiques, Université de Metz, F - 57045 Metz, France

E. Kaniuth
Affiliation: Fachbereich Mathematik/Informatik, Universität Paderborn, D - 33095 Paderborn, Germany

A. T. Lau
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1

G. Schlichting
Affiliation: Mathematisches Institut, Technische Universität München, D - 80290 München, Germany

Received by editor(s): December 15, 1995
Additional Notes: Work supported by NATO collaborative research grant CRG 940184
Dedicated: Dedicated to Professor Elmar Thoma on the occasion of his seventieth birthday
Article copyright: © Copyright 1997 American Mathematical Society