On a class of closed prime ideals in H^∞

Abstract

Gorkin and Mortini introduced the concept of k-hulls, k(x), of points x in M(H ^∞) ∖ ∖D, and studied the ideal structures of H ^∞ and H ^∞ +C. They posed a problem for which x∈ M(H ^∞) ∖ ∖D the set I(k(x)) is a closed prime ideal. In this article, we give a partial answer for sparse points x.

Keywords:

• Sparse Blaschke product
• QC-level set
• k-hull
• Prime ideal
• 1991 Mathematics Subject Classifications: 30D50
• 46J15

Acknowledgment

The first author was supported in part by Grant-in-Aid for Scientific Research (No. 16340037), Japan Society for the Promotion of Science.