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Spectral synthesis for $A(G)$ and subspaces of $VN(G)$

Authors: Eberhard Kaniuth and Anthony T. Lau
Journal: Proc. Amer. Math. Soc. 129 (2001), 3253-3263
MSC (2000): Primary 43A45, 43A46, 43A30, 22D15
Published electronically: April 9, 2001
MathSciNet review: 1845000
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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

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

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
Article copyright: © Copyright 2001 American Mathematical Society

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