Integral Equations and Operator Theory

, Volume 12, Issue 3, pp 324–342 | Cite as

A canonical form for self-adjoint pencils in Hilbert space

  • Paul Binding
Article
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Revised:

Abstract

We characterize those pencils P=λA−B of operators on a separable Hilbert space H for which a linear homeomorphism D of H exists satisfying the following: (i) H decomposes into a direct sum F+G, orthogonal in a (perhaps indefinite) inner product induced by A, where F is finite dimensional (ii) D*PD=PF⊕(λIG−C) where PF is a (congruence) canonical form for the general self-adjoint pencil on F, and C is a bounded self-adjoint operator on G. For a given P, explicit constructions are given for C, D, F, G and PF.

Keywords

Hilbert Space Canonical Form Explicit Construction Separable Hilbert Space Linear Homeomorphism 
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Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Paul Binding
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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