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Spectral Theory for Bounded Selfadjoint Operators

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

Abstract

A compact selfadjoint operator A acting on a Hilbert space can be represented in the form
$$ A = \sum\limits_j {\lambda _j \Delta E_{j,} } $$
(1)
where {λj} is the set of non-zero eigenvalues of A, the operator ΔEj is the orthogonal projection onto the eigenspace Ker(λj − A) and the series converges in the operator norm. The aim of this chapter is to obtain an analogous representation for an arbitrary bounded selfadjoint operator.

Keywords

Orthogonal Projection Analytic Continuation Spectral Theory Invariant Subspace Bounded Linear Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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