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Unbounded Fredholm Operators and Perturbation Theorems

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

Abstract

In this chapter the perturbation theory developed for bounded Fredholm operators in Sections XI.3 and XI.4 is extended to closed unbounded Fredholm operators. For the additive perturbation theorems this is accomplished via the simple device of renorming the domain of the operator T. In this way T becomes a bounded Fredholm operator to which the theorems of Chapter XI are applicable. We start with some properties and examples of the graph norm. The third and fourth section contain the main perturbation theorems. Section 5 presents a completeness theorem for certain compact perturbations of unbounded selfadjoint operators.

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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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