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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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