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

M. Langer, Heinz Langer, Alexander Markus, Christiane Tretter

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
Publication statusPublished - Mar 2008

Keywords

  • self-adjoint operator function
  • numerical range
  • spectrum
  • Virozub–Matsaev condition

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