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

DOI:
https://doi.org/10.1090/S0002-9939-1987-0875386-8

MathSciNet review:
875386

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Abstract: We consider the closed subalgebra of generated by the thin interpolating Blaschke products, the smallest subalgebra of containing , and the Douglas algebra generated by the complex conjugates of thin interpolating Blaschke products. Our main result is that every -invertible inner function is a finite product of thin interpolating Blaschke products, making . We apply results of Chang and Marshall to prove that , that finite convex combinations of finite products of thin interpolating Blaschke products are dense in the closed unit ball of , and that the corona theorem holds for .

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0875386-8

Article copyright:
© Copyright 1987
American Mathematical Society