In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-6,
author = {J. F. Feinstein},
title = {Trivial Jensen measures without regularity},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {67-74},
zbl = {1055.46035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-6}
}
J. F. Feinstein. Trivial Jensen measures without regularity. Studia Mathematica, Tome 147 (2001) pp. 67-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-6/