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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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