Extreme points of the unit ball of the FourierStieltjes algebra
Authors:
Peter F. Mah and Tianxuan Miao
Journal:
Proc. Amer. Math. Soc. 128 (2000), 10971103
MSC (1991):
Primary 43A30, 43A35, 43A65, 22D99
Published electronically:
August 5, 1999
MathSciNet review:
1637396
Fulltext PDF Free Access
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Abstract: Let be a locally compact group. Among other things, we proved in this paper that for an INgroup , the extreme points of the unit ball of the FourierStieltjes algebra are not in the Fourier algebra if and only if is noncompact, or equivalently, there is no irreducible representation of which is quasiequivalent to a subrepresentation of the left regular representation of if and only if is noncompact. This result is a noncommutative version of the following well known result: For any locally compact group , the extreme points of the unit ball of the measure algebra are not in the group algebra if and only if is nondiscrete. On the other hand, we also showed that if has the RNP, then there are extreme points of the unit ball of that are in . Since it is well known there are noncompact locally compact group for which has the RNP, there exist noncompact locally compact groups where extreme points of the unit ball of can be in . This shows that the condition be an INgroup cannot be entirely removed.
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Additional Information
Peter F. Mah
Affiliation:
Department of Mathematics and Statistics, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1
Email:
pfmah@mist.lakeheadu.ca
Tianxuan Miao
Affiliation:
Department of Mathematics and Statistics, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1
Email:
tmiao@thunder.lakeheadu.ca
DOI:
http://dx.doi.org/10.1090/S0002993999051047
PII:
S 00029939(99)051047
Keywords:
Locally compact groups,
extreme points,
weak$^{*}$strongly exposed points,
Fourier algebra,
FourierStieltjes algebra
Received by editor(s):
November 14, 1997
Received by editor(s) in revised form:
June 1, 1998
Published electronically:
August 5, 1999
Additional Notes:
This research is supported by an NSERC grant.
Dedicated:
Dedicated to Professor Edmond E. Granirer, with our admiration and respect,on the occasion of his retirement
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2000
American Mathematical Society
