Integral Equations and Operator Theory

, Volume 40, Issue 3, pp 342–381

Band-dominated operators with operator-valued coefficients, their Fredholm properties and finite sections

Authors

  • V. S. Rabinovich
    • Department of Mechanics and MathematicsRostov State University
    • Instituto Politecnico Nacional ESIME-Zacatenco SEPI
  • S. Roch
    • Fachbereich MathematikTechnische Universität Darmstadt
  • B. Silbermann
    • Fakultät für MathematikTechnische Universität Chemnitz
Article

DOI: 10.1007/BF01299850

Cite this article as:
Rabinovich, V.S., Roch, S. & Silbermann, B. Integr equ oper theory (2001) 40: 342. doi:10.1007/BF01299850

Abstract

The central theme of the present paper are band and band-dominated operators, i.e. norm limits of band operators. In the first part, we generalize the results from [24] and [25] concerning the Fredholm properties of band-dominated operators and the applicability of the finite section method to the case of operators with operator-valued coefficients. We characterize these properties in terms of the limit operators of the given band-dominated operator. The main objective of the second part is to apply these results to pseudodifferential operators on cones in ℝn which is possible after a suitable discretization.

MSC 2000

Primary 47 L 80Secondary 35 S 0547 A 5347 G 3065 R 20
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© Birkhäuser Verlag 2001