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/