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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weak*-closedness of subspaces of Fourier-Stieltjes algebras and weak*-continuity of the restriction map
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by M. B. Bekka, E. Kaniuth, A. T. Lau and G. Schlichting PDF
Trans. Amer. Math. Soc. 350 (1998), 2277-2296 Request permission

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
  • MR Author ID: 33840
  • 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
  • MR Author ID: 110640
  • Email: tlau@vega.math.ualberta.ca
  • G. Schlichting
  • Affiliation: Mathematisches Institut, Technische Universität München, D - 80290 München, Germany
  • Email: gschlich@mathematik.tu-muenchen.de
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2277-2296
  • MSC (1991): Primary 22D10, 43A30
  • DOI: https://doi.org/10.1090/S0002-9947-98-01835-2
  • MathSciNet review: 1401762