L∞ -representation spaces of hypergroups

L∞ - REPRESENTATION  SPACES OF HYPERGROUPS

R .Nasr-Isfahani

Abstract:  In the present paper, we initiate a stu dy o f  the L∞ - representations
o f  a hypergr oup X .  We i n trod uce and s tudy L∞ - representation  space R{X) o f  
X and then we prove that R{X) is identical with the space o f  inverse Fou r i e r -
Stieltjes transforms on X for a large class o f  hypergroups X. We also show
that this result is not valid in general.