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Abstract

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.