We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-4,
author = {Linus Carlsson and Urban Cegrell and Anders F\"allstr\"om},
title = {Spectrum of certain Banach algebras and [?]-problems},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {51-58},
zbl = {1117.32007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-4}
}
Linus Carlsson; Urban Cegrell; Anders Fällström. Spectrum of certain Banach algebras and ∂̅-problems. Annales Polonici Mathematici, Tome 92 (2007) pp. 51-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-4/