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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolation and Gleason parts in $ L$-domains


Author: Michael Frederick Behrens
Journal: Trans. Amer. Math. Soc. 286 (1984), 203-225
MSC: Primary 46J15; Secondary 03D55, 03H05, 30H05
MathSciNet review: 756036
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Abstract: We describe the closure of $ [ - 1/2,0)$ in the maximal ideal space $ \mathcal{M}(\mathcal{D})$ of $ {H^\infty }(\mathcal{D})$) for an arbitrary $ L$-domain $ \mathcal{D}$. For $ L$-domains satisfying $ \sup ({c_{n + 1}}/{c_n}) < 1$ and $ \Sigma {({r_n}/{c_n})^p} < \infty $, some $ p \geqslant 1$, we describe all interpolation sequences for $ {H^\infty }(\mathcal{D})$, we show that a homomorphism (except the distinguished homomorphism, when it exists) lies in a nontrivial Gleason part if and only if it is contained in the closure of an interpolating sequence, and we describe all the analytic structure occurring in $ \mathcal{M}(\mathcal{D})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0756036-X
PII: S 0002-9947(1984)0756036-X
Article copyright: © Copyright 1984 American Mathematical Society