Reiter nets for semidirect products of amenable groups and semigroups
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- by Benjamin Willson
- Proc. Amer. Math. Soc. 137 (2009), 3823-3832
- DOI: https://doi.org/10.1090/S0002-9939-09-09957-2
- Published electronically: July 14, 2009
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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.References
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Bibliographic Information
- Benjamin Willson
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
- Email: bwillson@math.ualberta.ca
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3823-3832
- MSC (2000): Primary 43A07, 22D05
- DOI: https://doi.org/10.1090/S0002-9939-09-09957-2
- MathSciNet review: 2529892