Self-adjoint analytic operator functions: Local spectral function and inner linearization

Heinz Langer, Alexander Markus, Vladimir Matsaev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub-Matsaev condition on some interval Δ0 and is boundedly invertible in the endpoints of Δ0, then the 'embedding' of the original Hilbert space H into the Hilbert space F, where the linearization of A(z) acts, is in fact an isomorphism between a subspace HΔ0 of H and F. As a consequence, properties of the local spectral function of A(z) on Δ0 and a so-called inner linearization of the operator function A(z) in the subspace H Δ0are established.

Original languageEnglish
Pages (from-to)533-545
Number of pages13
JournalIntegral Equations and Operator Theory
Volume63
Issue number4
DOIs
StatePublished - 1 Apr 2009

Keywords

  • Krein space
  • Linearization
  • Local spectral function
  • Self-adjoint analytic operator function
  • Spectrum of positive type

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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