Homomorphisms of l¹-algebras on signed polynomial hypergroups

Let {Rn} and {Pn} be two polynomial systems which induce signed polynomial hypergroup structures on N0. We investigate when the Banach algebra l1(N0, hR) can be continuously embedded into or is isomorphic to l1(N0, hP). We find sufficient conditions on the connection coefficients cnk given by Rn =Pnk=0 cnkPk, for the existence of such an embedding or isomorphism. Finally we apply these results to obtain amenability-properties of the l1-algebras induced by Bernstein-Szegö and Jacobi polynomials.