Spectral properties of unbounded J-self-adjoint block operator matrices

Matthias Langer, Michael Strauss

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Abstract

We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues.
Original languageEnglish
Pages (from-to)137-190
Number of pages54
JournalJournal of Spectral Theory
Volume7
Issue number1
DOIs
Publication statusPublished - 31 Mar 2017

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Keywords

  • J-self-adjoint operator
  • spectral enclosure
  • Schur complement
  • quadratic numerical range
  • Krein space
  • spectrum of positive type

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