Reiter's Condition P1 and Approximate Identities for Polynomial Hypergroups

Let K be a commutative hypergroup with the Haar measure μ. In the present paper we investigate whether the maximal ideals in L1(K,μ) 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∞(K,μ). Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.