An imprimitivity theorem for hypergroups
Let K be a hypergroup, H a closed subgroup of K such that K/H is paracompact and U a representation of K in a Hilbert space E. Let \(P: C_ 0(K/H)\to B(E)\) be an essental *-representation of the algebra \(C_ 0(K/H)\) such that \(U(a)P(g)=P(_ ag)U(a)\) for all \(a\in K\) and \(g\in C_ 0(K/H)\). The author establishes the existence of a unitary mapping \(W: E\to F\) such that \(WU(a)=U(a)W\) and \(WP(g)=P(g)W\) for all \(a\in K\) and \(g\in C_ 0(K/H)\).
scientific article; zbMATH DE number 4040529