, Volume 90, Issue 1, pp 89-114

Algebras generated by two bounded holomorphic functions

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Abstract

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, one of which is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension (of the closure) of such algebras. The conditions are expressed in terms of the inner part of a certain function which is explicitly derived from each pair of generators. Our results are based on identifyingz-invariant subspaces included in the closure of the algebra.

The second-named author thanks the University at Albany, Harvard University, and Brown University for their hospitality during the completion of this work.