Self-adjoint analytic operator functions and their local spectral function

H. Langer, A. Markus, V. Matsaev

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

For a self-adjoint analytic operator function A ( λ ), which satisfies on some interval Δ of the real axis the Virozub-Matsaev condition, a local spectral function Q on Δ, the values of which are non-negative operators, is introduced and studied. In the particular case that A ( λ ) = λ I - A with a self-adjoint operator A, it coincides with the orthogonal spectral function of A. An essential tool is a linearization of A ( λ ) by means of a self-adjoint operator in some Krein space and the local spectral function of this linearization. The main results of the paper concern properties of the range of Q ( Δ ) and the description of a natural complement of this range.

Original languageEnglish
Pages (from-to)193-225
Number of pages33
JournalJournal of Functional Analysis
Volume235
Issue number1
DOIs
StatePublished - 1 Jun 2006

Keywords

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

ASJC Scopus subject areas

  • Analysis

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