Spectrum of certain Banach algebras and -problems
Volume 90 / 2007
Annales Polonici Mathematici 90 (2007), 51-58
MSC: 32A65, 32W05, 46J20.
DOI: 10.4064/ap90-1-4
Abstract
We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain {\mit\Omega} where \overline\partial-problems with certain estimates can be solved. We show that the projection of the spectrum onto \mathbb C^n equals \,\overline{\!{\mit\Omega}} and that the fibers over {\mit\Omega} 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.
