Geodesic
Spectrum of certain Banach algebras and $\overline{\partial}$-problems
Linus Carlsson1 ; Urban Cegrell1 ; Anders Fällström1
1Department of Mathematics and Mathematical Statistics Umeå University S-901 87 Umeå, Sweden
Annales Polonici Mathematici, Tome 90 (2007) no. 1, pp. 51-58
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap90-1-4
Keywords: study spectrum certain banach algebras holomorphic functions defined domain mit omega where overline partial problems certain estimates solved projection spectrum mathbb equals overline mit omega fibers mit omega trivial solve corona problem special where generator continuous boundary

Linus Carlsson  1   ; Urban Cegrell  1   ; Anders Fällström  1

1 Department of Mathematics and Mathematical Statistics Umeå University S-901 87 Umeå, Sweden 
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Linus Carlsson; Urban Cegrell; Anders Fällström. Spectrum of certain Banach algebras and
$\overline{\partial}$-problems. Annales Polonici Mathematici, Tome 90 (2007) no. 1, pp. 51-58. doi: 10.4064/ap90-1-4

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