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Proceedings of the American Mathematical Society

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

 
 

 

Subalgebras of $C(M(H^ \infty ))$


Authors: A. Vol′berg, R. Younis and D. Zheng
Journal: Proc. Amer. Math. Soc. 123 (1995), 367-371
MSC: Primary 30D50; Secondary 30H05, 46J15
DOI: https://doi.org/10.1090/S0002-9939-1995-1221728-8
MathSciNet review: 1221728
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Abstract: In this paper we will provide a natural proof that if f is a bounded function that is harmonic but not analytic on $\mathbb {D}$, then ${H^\infty }(\mathbb {D})[f]$ contains $C(\overline {\mathbb {D}})$. We will also give a necessary and sufficient condition for a closed subalgebra of $C(M)$ to contain $C(\overline {\mathbb {D}})$.


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Article copyright: © Copyright 1995 American Mathematical Society