Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 30H05

Retrieve articles in all journals with MSC: 46J15, 30H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0801335-2
PII: S 0002-9939(1985)0801335-2
Article copyright: © Copyright 1985 American Mathematical Society