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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reiter nets for semidirect products of amenable groups and semigroups


Author: Benjamin Willson
Journal: Proc. Amer. Math. Soc. 137 (2009), 3823-3832
MSC (2000): Primary 43A07, 22D05
Published electronically: July 14, 2009
MathSciNet review: 2529892
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Abstract: In this paper we study Reiter nets for semidirect products of locally compact groups. A Reiter net is a net in $ L^1(G)^+_1$ which satisfies Reiter's condition (P1). These are nets of means which converge to left invariance in norm uniformly on compact subsets of $ G$. We provide two methods to combine Reiter nets for two groups to create a Reiter net for their semidirect product. We also present analogous results for combining Følner nets for locally compact groups and for Reiter nets for semidirect products of discrete semigroups.


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Additional Information

Benjamin Willson
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Email: bwillson@math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09957-2
PII: S 0002-9939(09)09957-2
Keywords: Reiter nets, semidirect product, strongly regular nets, F{\o }lner nets, amenable groups, semigroups
Received by editor(s): December 16, 2008
Received by editor(s) in revised form: March 3, 2009
Published electronically: July 14, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.