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Proceedings of the American Mathematical Society

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



The Forelli problem concerning ideals in the disk algebra $ A({\bf D})$

Author: Raymond Mortini
Journal: Proc. Amer. Math. Soc. 95 (1985), 261-264
MSC: Primary 46J15; Secondary 30H05
MathSciNet review: 801335
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Abstract: Let $ Z(f)$ be the zero set of a function $ f \in A({\mathbf{D}})$ and $ Z(I) = { \cap _{f \in I}}Z(f)$ the zero set of an ideal $ I$ in $ A({\mathbf{D}})$. It is shown that in the disk algebra $ A({\mathbf{D}})$ every finitely generated ideal $ I$ has the weak Forelli property, i.e. there exists a function $ f \in I$ such that $ Z(f) \cap T = Z(I) \cap T$, where $ T$ is the boundary of the unit circle $ {\mathbf{D}}$. On the other hand, there exists a finitely generated ideal $ I$ in $ A({\mathbf{D}})$ such that $ Z(f) \ne Z(I)$ for each choice of $ f \in I$. This provides us with a negative answer to a problem of F. Forelli [1].

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Article copyright: © Copyright 1985 American Mathematical Society