It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.
@article{bwmeta1.element.bwnjournal-article-apmv61z1p59bwm,
author = {Alexander J. Izzo},
title = {Exposed points in the set of representing measures for the disc algebra},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {59-62},
zbl = {0832.46047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p59bwm}
}
Alexander J. Izzo. Exposed points in the set of representing measures for the disc algebra. Annales Polonici Mathematici, Tome 62 (1995) pp. 59-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p59bwm/
[000] [B-W] R. Brummelhuis and J. Wiegerinck, Representing measures for the disc algebra and for the ball algebra, Ann. Polon. Math. 55 (1991), 19-35. | Zbl 0765.30035
[001] [R] J. Ryff, The support of representing measures for the disc algebra, in: Function Algebras, F. Birtel (ed.), Scott, Foresman and Company, Chicago, 1966. | Zbl 0144.37603