ALGEBRAS ASSOCIATED WITH BLASCHKE PRODUCTS OF TYPE G

CARROLL GUILLORY KIN Y. LI

Abstract. Let Ω and Ω_{fin} be the sets of all interpolating Blaschke products of type G and of finite type G, respectively. Let E and E_{fin} be the Douglas algebras generated by H^{∞} together with the complex conjugates of elements of Ω and Ω_{fin}, respectively. We show that the set of all invertible inner functions in E is the set of all finite products of elements of Ω , which is also the closure of Ω among the Blaschke products. Consequently, finite convex combinations of finite products of elements of Ω are dense in the closed unit ball of the subalgebra of H^{∞} generated by Ω. The same results hold when we replace Ω by Ω_{fin} and E by E_{fin}.