Spectral value sets of closed linear operators
Spectral value sets of closed linear operators
复制标题
闭线性算子的谱值集
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Pritchard
中科院分区：
文献类型：
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作者：
E. Gallestey;D. Hinrichsen;A. Pritchard
本文研究了复Banach空间上闭线性算子的谱在仿射扰动A <$AΔ = A + DΔE下的变化。这里A、D和E是给定的线性算子，而Δ是一个未知的有界线性算子，它参数化了可能的无界扰动DΔE。扰动算子AΔ的谱的并，当Δ的范数小于给定的δ > 0时，称为A在水平δ上的谱值集。在本文中，我们扩展了一个已知的矩阵情况下，这些集的特征到无限维，并在这样做，提出了一个框架，允许无界扰动的封闭线性算子的Banach空间。将通过将其应用于具有不确定参数的延迟系统和具有扰动边界条件的偏微分方程来说明结果。
We study how the spectrum of a closed linear operator on a complex Banach space changes under affine perturbations of the form A ↝ AΔ = A + DΔE. Here A, D and E are given linear operators, whereas Δ is an unknown bounded linear operator that parametrizes the possibly unbounded perturbation DΔE. The union of the spectra of the perturbed operators AΔ, with the norm of Δ smaller than a given δ > 0, is called the spectral value set of A at level δ. In this paper we extend a known characterization of these sets for the matrix case to infinite dimensions, and in so doing present a framework that allows for unbounded perturbations of closed linear operators on Banach spaces. The results will be illustrated by applying them to a delay system with uncertain parameters and to a partial differential equation with a perturbed boundary condition.