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

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

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 b...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 129; no. 11; pp. 3253 - 3263
Main Authors: Kaniuth, Eberhard, Lau, Anthony T.
Format: Journal Article
Language:English
Published: American Mathematical Society 01-11-2001
Subjects:
Algebra
Mathematical functions
Mathematical theorems
Von Neumann algebra
Online Access:Get full text
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-01-05924-X