Remarks on resolvent positive operators and their perturbation
Remarks on resolvent positive operators and their perturbation
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DOI：
10.3934/dcds.1998.4.73
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发表时间：
1997-10
影响因子：
1.1
通讯作者：
H. Thieme
中科院分区：
文献类型：
--
作者：
H. Thieme
考虑预解式正算子B被正算子C：D（A）~ X的正扰动A = B+ C，特别研究了它们的谱性质.我们用预解式输出F（\lambda）= C（\lambda - B）^{-1}$刻画了$A$，$s（A）$的谱界，并导出了$s（A）$是$A$的特征值和$A$的预解式的（一阶）极点的条件.在我们的方法中，我们证明了一个完全单调算子族的谱半径形成一个超凸函数。我们的结果将被用于在即将出版的研究谱和大时间性质的正算子半群。
We consider positive perturbations $A = B+ C $ of resolvent positive operators $B$ by positive operators $C: D(A) \to X$ and in particular study their spectral properties. We characterize the spectral bound of $A$, $s(A)$, in terms of the resolvent outputs $F(\lambda) = C (\lambda - B)^{-1}$ 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 monotonic 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.