Spectrum of certain Banach algebras and $\overline{\partial}$-problems

Volume 90 / 2007

Linus Carlsson, Urban Cegrell, Anders Fällström 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.

Authors

  • Linus CarlssonDepartment of Mathematics and Mathematical Statistics
    Umeå University
    S-901 87 Umeå, Sweden
    e-mail
  • Urban CegrellDepartment of Mathematics and Mathematical Statistics
    Umeå University
    S-901 87 Umeå, Sweden
    e-mail
  • Anders FällströmDepartment of Mathematics and Mathematical Statistics
    Umeå University
    S-901 87 Umeå, Sweden
    e-mail

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