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CONFIGURATIONS AND INVARIANT NETS FOR AMENABLE HYPERGROUPS AND RELATED ALGEBRAS.

Authors :
WILLSON, BENJAMIN
Source :
Transactions of the American Mathematical Society; Oct2014, Vol. 366 Issue 10, p5087-5112, 26p
Publication Year :
2014

Abstract

Let H be a hypergroup with left Haar measure. The amenability of H can be characterized by the existence of nets of positive, norm one functions in L¹(H) which tend to left invariance in any of several ways. In this paper we present a characterization of the amenability of H using configuration equations. Extending work of Rosenblatt and Willis, we construct, for a certain class of hypergroups, nets in L1(H) which tend to left invariance weakly, but not in norm. We define the semidirect product of H with a locally compact group. We show that the semidirect product of an amenable hypergroup and an amenable locally compact group is an amenable hypergroup and show how to construct Reiter nets for this semidirect product. These results are generalized to Lau algebras, providing a new characterization of left amenability of a Lau algebra and a notion of a semidirect product of a Lau algebra with a locally compact group. The semidirect product of a left amenable Lau algebra with an amenable locally compact group is shown to be a left amenable Lau algebra. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029947
Volume :
366
Issue :
10
Database :
Complementary Index
Journal :
Transactions of the American Mathematical Society
Publication Type :
Academic Journal
Accession number :
97414727
Full Text :
https://doi.org/10.1090/S0002-9947-2014-05731-0