The exposed points of the set

of invariant means on an ideal

Author:
Tianxuan Miao

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3571-3579

MSC (1991):
Primary 43A07

MathSciNet review:
1468200

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -compact locally compact nondiscrete group and let be a -invariant ideal of . We denote the set of left invariant means on that are zero on (i.e. for all ) by . We show that, when is amenable as a discrete group and the closed -invariant subset of the spectrum of corresponding to is a -set, is very large in the sense that every nonempty -subset of contains a norm discrete copy of , where is the Stone- compactification of the set of positive integers with the discrete topology. In particular, we prove that has no exposed points in this case and every nonempty -subset of the set of left invariant means on contains a norm discrete copy of .

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Additional Information

**Tianxuan Miao**

Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada P7E 5E1

Email:
tmiao@thunder.lakeheadu.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04550-X

Keywords:
Locally compact groups,
amenable groups,
invariant means,
invariant ideals,
exposed points

Received by editor(s):
December 12, 1996

Received by editor(s) in revised form:
April 20, 1997

Additional Notes:
This research is supported by an NSERC grant.

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1998
American Mathematical Society