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 - 1998 |
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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
- Mathematics(all)
- Analysis
- Applied Mathematics
- Discrete Mathematics and Combinatorics
Cite this
Remarks on resolvent positive operators and their perturbation. / Thieme, Horst.
In: Discrete and Continuous Dynamical Systems, Vol. 4, No. 1, 1998, p. 73-90.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Remarks on resolvent positive operators and their perturbation
AU - Thieme, Horst
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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.
KW - Asynchronous exponential growth
KW - Balanced exponential growth
KW - Growth bounds
KW - Integrated semigroups
KW - Positive perturbation
KW - Resolvent outputs
KW - Resolvent positive operators
KW - Semigroups
KW - Spectral bound
UR - http://www.scopus.com/inward/record.url?scp=0032352740&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032352740&partnerID=8YFLogxK
M3 - Article
VL - 4
SP - 73
EP - 90
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
SN - 1078-0947
IS - 1
ER -