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

Canadian mathematical bulletin

Benjamin Willson¹ 

[1] Department of Mathematics , Hanyang University , 222 Wangsimni-ro, Seongdong-gu , Seoul, Korea

关键词: invariant measure;    Haar measure;    hypergroup;    amenability;    function translations;   

DOI  :  10.4153/CMB-2014-069-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we present a fixed point property for amenablehypergroups which is analogous to Rickert's fixed point theoremfor semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functionsto the existence of a fixed point for any action of the hypergroup. Using this fixed point property, a certain class of hypergroupsare shown to have a left Haar measure.

【 授权许可】

Unknown