CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability

  Published:2015-03-05
 Printed: Jun 2015
  • Benjamin Willson,
    Department of Mathematics , Hanyang University , 222 Wangsimni-ro, Seongdong-gu , Seoul, Korea
Format:   LaTeX   MathJax   PDF  

Abstract

In this paper we present a fixed point property for amenable hypergroups which is analogous to Rickert's fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, a certain class of hypergroups are shown to have a left Haar measure.
Keywords: invariant measure, Haar measure, hypergroup, amenability, function translations invariant measure, Haar measure, hypergroup, amenability, function translations
MSC Classifications: 43A62, 43A05, 43A07 show english descriptions Hypergroups
Measures on groups and semigroups, etc.
Means on groups, semigroups, etc.; amenable groups
43A62 - Hypergroups
43A05 - Measures on groups and semigroups, etc.
43A07 - Means on groups, semigroups, etc.; amenable groups
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/