In [6] 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-4,
author = {M. J. Heath},
title = {A note on a construction of J. F. Feinstein},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {63-70},
zbl = {1088.46025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-4}
}
M. J. Heath. A note on a construction of J. F. Feinstein. Studia Mathematica, Tome 166 (2005) pp. 63-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-1-4/