Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups
Author:
Ching Chou
Journal:
Trans. Amer. Math. Soc. 274 (1982), 141-157
MSC:
Primary 43A60
DOI:
https://doi.org/10.1090/S0002-9947-1982-0670924-2
MathSciNet review:
670924
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Abstract | References | Similar Articles | Additional Information
Abstract: A noncompact locally compact group is called an Eberlein group if
where
is the algebra of continuous weakly almost periodic functions on
and
is the uniform closure of the Fourier-Stieltjes algebra of
. We show that if
is a noncompact
-group or a noncompact nilpotent group then
contains a linear isometric copy of
. In particular,
is not an Eberlein group. On the other hand, finite direct products of Euclidean motion groups and, by a result of W. Veech, noncompact semisimple analytic groups with finite centers are Eberlein groups.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0670924-2
Keywords:
Locally compact groups,
weakly almost periodic functions,
Fourier-Stieltjes algebras,
unitary representations,
weak Sidon sets,
relatively dense sets,
-algebras,
-groups,
nilpotent groups,
motion groups,
semisimple groups,
weakly almost periodic compactification
Article copyright:
© Copyright 1982
American Mathematical Society