Acute and Stable Perturbations of the Drazin Inverse of Bounded Linear Operators in Banach Spaces
Acute and Stable Perturbations of the Drazin Inverse of Bounded Linear Operators in Banach Spaces
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DOI：
10.1080/01630563.2020.1813162
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发表时间：
2020-09
影响因子：
1.2
通讯作者：
Haifeng Ma
中科院分区：
文献类型：
--
作者：
Haifeng Ma
设Banach空间X上有界线性算子的集合，且线性算子是Drazin可逆的。如果B是Drazin可逆且可逆，则线性算子是A的稳定扰动，其中I是X上的恒等算子，分别是A和B的谱投影。在矩阵B是矩阵A的稳定摄动的类似条件下，Xu， Song和Wei（方阵的Drazin逆的稳定摄动，SIAM J. matrix Anal）导出了Drazin逆BD的显式公式。达成。科学进展，31（3)(2010),pp. 1507-1520）。将该公式推广到无限维情况，并将有限维情况下的谱半径的一些新公式推广到Banach空间。
Abstract Let be the set of bounded linear operators on a Banach space X, and a liner operator be Drazin invertible. A linear operator is said to be a stable perturbation of A if B is Drazin invertible and is invertible, where I is the identity operator on X, and are the spectral projectors of A and B respectively. We call B an acute perturbation of A with respect to the Drazin inverse if the spectral radius Under the similar condition that a matrix B is a stable perturbation of a matrix A, an explicit formula for the Drazin inverse BD is derived by Xu, Song and Wei (The stable perturbation of the Drazin inverse of the square matrices, SIAM J. Matrix Anal. Appl., 31(3) (2010), pp. 1507-1520). This formula is generalized to the infinite-dimensional case, and some new formulas for spectral radius of is generalized from the finite-dimensional case to the Banach space.