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A counterexample for $H^{\infty}$ approximable functions

Author: Daniel Suárez
Journal: Proc. Amer. Math. Soc. 128 (2000), 3003-3007
MSC (2000): Primary 30E10; Secondary 30H05
Published electronically: April 28, 2000
MathSciNet review: 1707532
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Let $\mathbb{D}$ be the unit disk. We show that for some relatively closed set $F\subset \mathbb{D}$ there is a function $f$ that can be uniformly approximated on $F$ by functions of $H^{\infty}$, but such that $f$ cannot be written as $f= h+g$, with $h\in H^{\infty}$ and $g$ uniformly continuous on $F$. This answers a question of Stray.

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Additional Information

Daniel Suárez
Affiliation: Departamento de Matemática, Facultad de Cs. Exactas y Naturales, UBA, Pab. I, Ciudad Universitaria, (1428) Núñez, Capital Federal, Argentina
Address at time of publication: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain

Keywords: Bounded analytic functions, uniform approximation
Received by editor(s): December 8, 1998
Published electronically: April 28, 2000
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society

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