Subalgebras of 𝐶(𝑀(𝐻^{∞}))

Vol′berg, A.; Younis, R.; Zheng, D.

doi:10.1090/S0002-9939-1995-1221728-8

Subalgebras of $C(M(H^ \infty ))$
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by A. Vol′berg, R. Younis and D. Zheng PDF

Proc. Amer. Math. Soc. 123 (1995), 367-371 Request permission

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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