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)


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.


Band-dominated operators finite sections stability limit operators 


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  1. [1]
    M. Lindner, Infinite Matrices and their Finite Sections. An Introduction to the Limit Operator Method. Birkhäuser, Basel, Boston, Berlin 2006.Google Scholar
  2. [2]
    V.S. Rabinovich, S. Roch, B. Silbermann, Fredholm theory and finite section method for band-dominated operators. Integral Equations Oper. Theory 30(1998), 4, 452–495.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    V.S. Rabinovich, S. Roch, B. Silbermann, Algebras of approximation sequences: Finite sections of band-dominated operators. Acta Appl. Math. 65(2001), 315–332.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    V.S. Rabinovich, S. Roch, B. Silbermann, Limit Operators and Their Applications in Operator Theory. Operator Theory: Adv. and Appl. 150, Birkhäuser Verlag, Basel, Boston, Berlin 2004.Google Scholar
  5. [5]
    S. Roch, Finite sections of band-dominated operators. Preprint 2355 TU Darmstadt, July 2004, 98 p., to appear in Memoirs Amer. Math. Soc.Google Scholar
  6. [6]
    J. Roe, Band-dominated Fredholm operators on discrete groups. Integral Equations Oper. Theory 51 (2005), 3, 411–416.zbMATHCrossRefMathSciNetGoogle Scholar

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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