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.

中文翻译：

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Banach空间中有界线性算子的Drazin逆的急性和稳定摄动

摘要 设 是 Banach 空间 X 上的一组有界线性算子，线性算子是 Drazin 可逆的。如果 B 是 Drazin 可逆且可逆的，则称线性算子是 A 的稳定扰动，其中 I 是 X 上的恒等算子，并且分别是 A 和 B 的光谱投影。我们称 B 是 A 相对于 Drazin 逆的急性扰动，如果谱半径在矩阵 B 是矩阵 A 的稳定扰动的类似条件下，Drazin 逆 BD 的显式公式由 Xu、Song 和Wei（方阵 Drazin 逆的稳定扰动，SIAM J. Matrix Anal. Appl.，31(3) (2010)，pp. 1507-1520）。这个公式推广到无限维的情况，