Algebras generated by two bounded holomorphic functions

Details Algebras generated by two bounded holomorphic functions Algebras generated by two bounded holomorphic functions

2001-01-21

arxiv.org/abs/math/0101171v2

Mathematics

Complex Variables

22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Anal

Scientific paper

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

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