Notes on Certain Star-Shift Invariant Subspaces

  • John R. Akeroyd
  • Kristi Karber


Our work addresses the question: for which (infinite) Blaschke products B does the star-shift invariant subspace K b:= H 2(D) Θ BH 2(D) contain a (non-trivial) function with a non-trivial singular inner factor? In the case that the zeros of B have only finitely many accumulation points w 1,w 2, …, w n in T, a recent paper shows that, for an affirmative answer, there necessarily exist k, 1 ≤ kn, and a subsequence of the zeros of B that converges tangentially to w k on “both sides” of w k. One of the results in this article improves upon this theorem. And, currently, the only examples of Blaschke products in the literature that are shown to yield an affirmative answer are those that have a proper factor b that satisfies b(D) ≠ D. We produce many examples here that have no such factor.

Key Words

backward shift inner function 

2000 MSC

30H05 47B38 49J20 


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Copyright information

© Heldermann  Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArkansasFayettevilleUSA

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