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Transactions of the American Mathematical Society
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
Email: bekka@poncelet.univ-metz.fr

E. Kaniuth
Affiliation: Fachbereich Mathematik/Informatik, Universität Paderborn, D - 33095 Paderborn, Germany
Email: kaniuth@uni-paderborn.de

A. T. Lau
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1
Email: tlau@vega.math.ualberta.ca

G. Schlichting
Affiliation: Mathematisches Institut, Technische Universität München, D - 80290 München, Germany
Email: gschlich@mathematik.tu-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01835-2
PII: S 0002-9947(98)01835-2
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