## Thin interpolating sequences and three algebras of bounded functions

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- by Håkan Hedenmalm
- Proc. Amer. Math. Soc.
**99**(1987), 489-495 - DOI: https://doi.org/10.1090/S0002-9939-1987-0875386-8
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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 ${\mathbf {A}}$.## References

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## Bibliographic Information

- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**99**(1987), 489-495 - MSC: Primary 46J15; Secondary 30H05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0875386-8
- MathSciNet review: 875386