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On Finite Sections of Band-dominated Operators

  • Vladimir S. Rabinovich
  • Steffen Roch
  • Bernd Silbermann
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)

Abstract

In an earlier paper we showed that the sequence of the finite sections P n AP n of a band-dominated operator A on l p (ℤ) is stable if and only if the operator A is invertible, every limit operator of the sequence (P n AP n ) is invertible, and if the norms of the inverses of the limit operators are uniformly bounded. The purpose of this short note is to show that the uniform boundedness condition is redundant.

Keywords

Band-dominated operators finite sections stability limit operators 

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References

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Vladimir S. Rabinovich
    • 1
  • Steffen Roch
    • 2
  • Bernd Silbermann
    • 3
  1. 1.Instituto Politechnico NationalESIME-ZacatencoMexico, D.F.Mexico
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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