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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral synthesis for $A(G)$ and subspaces of $VN(G)$
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by Eberhard Kaniuth and Anthony T. Lau PDF
Proc. Amer. Math. Soc. 129 (2001), 3253-3263 Request permission


Let $G$ be a locally compact group, $A(G)$ the Fourier algebra of $G$ and $VN(G)$ the von Neumann algebra generated by the left regular representation of $G$. We introduce the notion of $X$-spectral set and $X$-Ditkin set when $X$ is an $A(G)$-invariant linear subspace of $VN(G)$, thus providing a unified approach to both spectral and Ditkin sets and their local variants. Among other things, we prove results on unions of $X$-spectral sets and $X$-Ditkin sets, and an injection theorem for $X$-spectral sets.
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Additional Information
  • Eberhard Kaniuth
  • Affiliation: Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany
  • Email:
  • Anthony T. Lau
  • Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • MR Author ID: 110640
  • Email:
  • Received by editor(s): June 19, 1999
  • Received by editor(s) in revised form: March 10, 2000
  • Published electronically: April 9, 2001
  • Additional Notes: Supported by NATO collaborative research grant CRG 940184. The first author has also been supported by a travel grant from the German Research Foundation (DFG), and the second author is also supported by NSERC grant A7679
  • Communicated by: Dale Alspach
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3253-3263
  • MSC (2000): Primary 43A45, 43A46, 43A30, 22D15
  • DOI:
  • MathSciNet review: 1845000