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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A counterexample to a conjecture of S. E. Morris


Author: J. F. Feinstein
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2389-2397
MSC (2000): Primary 46J10, 46H20
Published electronically: February 20, 2004
MathSciNet review: 2052417
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Abstract: We give a counterexample to a conjecture of S. E. Morris by showing that there is a compact plane set $X$ such that $R(X)$ has no nonzero, bounded point derivations but such that $R(X)$ is not weakly amenable. We also give an example of a separable uniform algebra $A$ such that every maximal ideal of $A$ has a bounded approximate identity but such that $A$ is not weakly amenable.


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Additional Information

J. F. Feinstein
Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, England
Email: Joel.Feinstein@nottingham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07382-4
PII: S 0002-9939(04)07382-4
Received by editor(s): May 12, 2003
Published electronically: February 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society