Compact Hypergroup Characters and Finite Universal Korovkin Sets in L 1-Hypergroup Algebra

Abstract

Let K be a compact hypergroup.We investigate Trig(K), the linear span of coordinate functions of the irreducible representations of K. Contrary to the group case, Trig(K) endowed with the usual multiplication does not bear an algebra structure, but it has a natural normed algebra structure when it inherits the convolution from $$\mathcal {M}(K)$$ , the algebra of all bounded Radon measures. We characterize the center of the algebras $$\mathcal {M}(K)$$ , L p (K) and Trig(K) respectively, and consequently we obtain, for a certain class of hypergroups, the correspondence between the structure space of the center of L 1(K) and the center of Trig(K). As an application we study the existence of a finite universal Korovkin set w.r.t. positive operators in the center of L 1(K), in particular in L 1(K), whenever K is commutative.