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Spectral synthesis for  and subspaces of 
Author(s):
Eberhard
Kaniuth;
Anthony
T.
Lau
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3253-3263.
MSC (2000):
Primary 43A45, 43A46, 43A30, 22D15
Posted:
April 9, 2001
MathSciNet review:
1845000
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Abstract:
Let  be a locally compact group,  the Fourier algebra of  and  the von Neumann algebra generated by the left regular representation of  . We introduce the notion of  -spectral set and  -Ditkin set when  is an  -invariant linear subspace of  , thus providing a unified approach to both spectral and Ditkin sets and their local variants. Among other things, we prove results on unions of  -spectral sets and  -Ditkin sets, and an injection theorem for  -spectral sets.
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Additional Information:
Eberhard
Kaniuth
Affiliation:
Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany
Email:
kaniuth@uni-paderborn.de
Anthony
T.
Lau
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email:
tlau@math.ualberta.ca
DOI:
10.1090/S0002-9939-01-05924-X
PII:
S 0002-9939(01)05924-X
Received by editor(s):
June 19, 1999
Received by editor(s) in revised form:
March 10, 2000
Posted:
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 of article:
Copyright
2001,
American Mathematical Society
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