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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Thin interpolating sequences and three algebras of bounded functions


Author: Håkan Hedenmalm
Journal: Proc. Amer. Math. Soc. 99 (1987), 489-495
MSC: Primary 46J15; Secondary 30H05
MathSciNet review: 875386
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Abstract: We consider the closed subalgebra $ {\mathbf{A}}$ of $ {H^\infty }$ generated by the thin interpolating Blaschke products, the smallest $ {C^*}$ subalgebra $ {\mathbf{B}}$ of $ {L^\infty }$ containing $ {\mathbf{A}}$, and the Douglas algebra $ {\mathbf{E}}$ generated by the complex conjugates of thin interpolating Blaschke products. Our main result is that every $ {\mathbf{E}}$-invertible inner function is a finite product of thin interpolating Blaschke products, making $ {\mathbf{B}} = {C_{\mathbf{E}}}$. We apply results of Chang and Marshall to prove that $ {\mathbf{A}} = {\mathbf{B}} \cap {H^\infty }$, that finite convex combinations of finite products of thin interpolating Blaschke products are dense in the closed unit ball of $ {\mathbf{A}}$, and that the corona theorem holds for $ {\mathbf{A}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875386-8
PII: S 0002-9939(1987)0875386-8
Article copyright: © Copyright 1987 American Mathematical Society