Invariant nets for amenable groups and hypergroups

• Author / Creator

  Willson, Benjamin

• 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.

• Subjects / Keywords

  • Folner net
  • Lau algebra
  • Amenable
  • Reiter Net
  • Semidirect product
  • Hypergroups

• Graduation date

  Fall 2011

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R33931

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.