Algebras generated by two bounded holomorphic functions

  • Michael I. Stessin
  • Pascal J. Thomas
Article

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.

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Copyright information

© Hebrew University of Jerusalem 2003

Authors and Affiliations

  • Michael I. Stessin
    • 1
  • Pascal J. Thomas
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity at AlbanyAlbanyUSA
  2. 2.Laboratoire Emile Picard, UMR CNRS 5580Toulouse CedexFrance

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