A note on a construction of J. F. Feinstein

Tom 169 / 2005

M. J. Heath Studia Mathematica 169 (2005), 63-70 MSC: Primary 46J10; Secondary 46H25. DOI: 10.4064/sm169-1-4


In \cite{F} J. F. Feinstein constructed a compact plane set $X$ such that $R(X)$, the uniform closure of the algebra of rational functions with poles off $X$, has no non-zero, bounded point derivations but is not weakly amenable. In the same paper he gave an example of a separable uniform algebra $A$ such that every point in the character space of $A$ is a peak point but $ A$ is not weakly amenable. We show that it is possible to modify the construction in order to produce examples which are also regular.


  • M. J. HeathSchool of Mathematical Sciences
    University of Nottingham
    Nottingham NG7 2RD, England

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