Reiter's condition P1 and approximate identities for polynomial hypergroups

Let K be a commutative hypergroup with the Haar measure mu. In the present paper we investigate whether the maximal ideals in L-1 (K, mu) have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L-infinity (K, mu). Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.