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Invariant nets for amenable groups and hypergroups Open Access


Other title
Lau algebra
Reiter Net
semidirect product
Folner net
Type of item
Degree grantor
University of Alberta
Author or creator
Willson, Benjamin
Supervisor and department
Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
Examining committee member and department
Lasser, Rupert (Munich University of Technology)
Dai, Feng (Math & Stats)
Stewart, Lorna (Computing Science)
Litvak, Alexander (Math & Stats)
Schmuland, Byron (Math & Stats)
Department of Mathematical and Statistical Sciences

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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 L^1(H) which tend to left invariance in any of several ways. In this thesis 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 L^1(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. Some results towards the existence of a left Haar measure for amenable hypergroups are proven.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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