The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

Heinz Langer, Matthias Langer, Alexander Markus, Christiane Tretter

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.

Original languageEnglish
Pages (from-to)99-134
Number of pages36
JournalComplex Analysis and Operator Theory
Volume2
Issue number1
DOIs
StatePublished - 1 Mar 2008

Keywords

  • Numerical range
  • Self-adjoint operator function
  • Spectrum

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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