Abstract
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 language | English |
|---|---|
| Pages (from-to) | 89-112 |
| Number of pages | 24 |
| Journal | Linear Algebra and Its Applications |
| Volume | 330 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - 15 Jun 2001 |
Keywords
- 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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