Open subgroups of and almost periodic functionals on

Author:
Zhiguo Hu

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2473-2478

MSC (1991):
Primary 22D25, 43A30

Published electronically:
February 25, 2000

MathSciNet review:
1662249

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Abstract | References | Similar Articles | Additional Information

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/S0002-9939-00-05299-0

Keywords:
Locally compact groups,
left regular representation,
Fourier and Fourier-Stieltjes 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