A new concept for block operator matrices:The quadratic numerical range

H. Langer, A. Markus, V. Matsaev, C. Tretter

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


In this paper a new concept for 2×2-block operator matrices - the quadratic numerical range - is studied. The main results are a spectral inclusion theorem, an estimate of the resolvent in terms of the quadratic numerical range, factorization theorems for the Schur complements, and a theorem about angular operator representations of spectral invariant subspaces which implies e.g. the existence of solutions of the corresponding Riccati equations and a block diagonalization. All results are new in the operator as well as in the matrix case.

Original languageEnglish
Pages (from-to)89-112
Number of pages24
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - 15 Jun 2001


  • Angular operator
  • Block operator matrix
  • Quadratic numerical range
  • Riccati equation
  • Schur complement

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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