Abstract
We consider positive perturbations A = B + C of resolvent positive operators B by positive operators C : D(A) → X and in particular study their spectral properties. We characterize the spectral bound of A, s(A), in terms of the resolvent outputs F(λ) = C(λ - B)-1 and derive conditions for s(A) to be an eigenvalue of A and a (first order) pole of the resolvent of A. On our way we show that the spectral radii of a completely monotonie operator family form a superconvex function. Our results will be used in forthcoming publications to study the spectral and large-time properties of positive operator semigroups.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 73-90 |
| Number of pages | 18 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 4 |
| Issue number | 1 |
| State | Published - Dec 1 1998 |
Keywords
- Asynchronous exponential growth
- Balanced exponential growth
- Growth bounds
- Integrated semigroups
- Positive perturbation
- Resolvent outputs
- Resolvent positive operators
- Semigroups
- Spectral bound
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics