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Linear Operator Pencils

  • Israel Gohberg
  • Seymour Goldberg
  • Marinus A. Kaashoek
Part of the Operator Theory: Advances and Applications book series (OT, volume 49)

Abstract

In this chapter we study linear pencils λGA, where G and A are bounded linear operators acting between complex Banach spaces X and Y. The simplest example is the case when X = Y and G = I, the identity operator on X. This case was already considered in the previous chapters. If G is invertible, then spectral problems concerning the pencil λGA are easily reduced to those of λIG −1 A. In this chapter we consider the more general case when G is not invertible, but we assume that the pencil is regular, i.e., for some λ 0 ∈ ℂ the operator λ 0 GA is invertible.

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Copyright information

© Springer Basel AG 1990

Authors and Affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Marinus A. Kaashoek
    • 3
  1. 1.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands

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