We give a simple complex-variable proof of an old result of Zemánek and Le Page on the radical of a Banach algebra. Incidentally, the argument also proves a recent result of Harris and Kadison.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-2,
author = {Graham R. Allan},
title = {An analytic approach to the spectral characterization of the radical},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {11-14},
zbl = {1152.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-2}
}
Graham R. Allan. An analytic approach to the spectral characterization of the radical. Studia Mathematica, Tome 187 (2008) pp. 11-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-2/