Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)

H. Langer, A. Markus, V. Matsaev

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations

Abstract

In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression Aδ(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression Aδ(z) are established.

Original languageEnglish
Title of host publicationA Panorama of Modern Operator Theory and Related Topics
Subtitle of host publicationThe Israel Gohberg Memorial Volume
PublisherSpringer Basel
Pages445-463
Number of pages19
ISBN (Electronic)9783034802215
ISBN (Print)9783034802208
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Factorization
  • Linearization
  • Self-adjoint analytic operator function
  • Spectral function
  • Spectrum of definite type

ASJC Scopus subject areas

  • Mathematics (all)

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