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    STUDIA MATHEMATICA - Issue no. 2 / 2016  
         
  Article:   INNER AMENABLE HYPERGROUPS, INVARIANT PROJECTIONS AND HAHN-BANACH EXTENSION THEOREM RELATED TO HYPERGROUPS.

Authors:  .
 
       
         
  Abstract:   Let K be a hypergroup with a Haar measure. In the present paper we initiate the study of inner amenable hypergroups extending amenable hypergroups and inner amenable locally compact groups. We also provide characterizations of amenable hypergroups by hypergroups having the Hahn-Banach extension or monotone projection property. Finally we focus on weak*-invariant complemented subspaces of L¥(K).

Mathematics Subject Classi cation (2010): 43A07.

Keywords: Hypergroup, inner amenability, quasi central, approximate identity, asymptotically central, semidirect product hypergroup, strong ergodicity, Hahn-Banach extension property, monotone extension property, partially ordered real Banach space; amenability, real version of amenability, multiplicative left invariant mean.
 
         
     
         
         
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