On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces
On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces
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DOI：
10.1016/j.jmaa.2007.10.066
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发表时间：
2008-05
影响因子：
1.3
通讯作者：
N. Castro-González;J. Y. Vélez-Cerrada
中科院分区：
文献类型：
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作者：
N. Castro-González;J. Y. Vélez-Cerrada
给定Banach空间X上具有Drazin逆AD和指标r的有界算子a，研究了一类群可逆有界算子B，使得I+AD（B−a）可逆且r (B)∩N(Ar)={0}。我们证明了它们可以写成分解为X=R(Ar)⊕N（Ar）的矩阵算子，B=(B1B12B21B21B1−1B12)，其中b1和B12+ b12b21是可逆的。建立了扰动算子的几个特征，推广了矩阵结果。我们分析了Drazin逆的扰动，并给出了‖b#−AD‖和‖BB #−ADA‖的显式上界。得到了Banach空间上算子群逆连续性的一个结果。
Given a bounded operator A on a Banach space X with Drazin inverse ADand index r, we study the class of group invertible bounded operators B such that I+AD(B−A) is invertible and R(B)∩N(Ar)={0}. We show that they can be written with respect to the decomposition X=R(Ar)⊕N(Ar) as a matrix operator, B=(B1B12B21B21B1−1B12), where B1and B12+B12B21are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of ‖B♯−AD‖ and ‖BB♯−ADA‖. We obtain a result on the continuity of the group inverse for operators on Banach spaces.