Open subgroups of and almost periodic functionals on
Author:
Zhiguo Hu
Journal:
Proc. Amer. Math. Soc. 128 (2000), 24732478
MSC (1991):
Primary 22D25, 43A30
Published electronically:
February 25, 2000
MathSciNet review:
1662249
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Abstract: Let be a locally compact group and let denote the algebra generated by left translation operators on . Let and be the spaces of almost periodic and weakly almost periodic functionals on the Fourier algebra , respectively. It is shown that if contains an open abelian subgroup, then (1) if and only if is norm dense in ; (2) is a algebra if is norm dense in , where denotes the set of elements in with compact support. In particular, for any amenable locally compact group which contains an open abelian subgroup, has the dual Bohr approximation property and is a algebra.
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Additional Information
Zhiguo Hu
Affiliation:
Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
Email:
zhiguohu@uwindsor.ca
DOI:
http://dx.doi.org/10.1090/S0002993900052990
PII:
S 00029939(00)052990
Keywords:
Locally compact groups,
left regular representation,
Fourier and FourierStieltjes algebras,
almost periodic functionals,
weakly almost periodic functionals,
amenable groups
Received by editor(s):
December 3, 1997
Received by editor(s) in revised form:
September 8, 1998
Published electronically:
February 25, 2000
Additional Notes:
This research was supported by an NSERC grant
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2000
American Mathematical Society
