Geodesic
Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces
Yifeng Xue1 ; Jianbing Cao2 ; Yifeng Xue ; Jianbing Cao
1Department of Mathematics, East China Normal University
2Department of Mathematics, Henan Institute of Science and Technology Xinxiang, Henan, 453003
Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 181-194 
Yifeng Xue; Jianbing Cao; Yifeng Xue; Jianbing Cao. Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 181-194. http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a2/
@article{AMUC_2014_83_2_a2,
     author = {Yifeng Xue and Jianbing Cao and Yifeng Xue and Jianbing Cao},
     title = { Perturbation analysis of bounded homogeneous generalized inverses on {Banach} spaces},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {181--194},
     year = {2014},
     volume = {83},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a2/}
}
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Let $X, Y$ be Banach spaces and $T: X \to Y$ be a bounded linear operator. In this paper, we initiate the study of the perturbation problems for bounded homogeneous generalized inverse $T^h$ and quasi-linear projector generalized inverse $T^H$ of $T$. Some applications to the representations and perturbations of the Moore-Penrose metric generalized inverse $T^M$ of $T$ are also given. The obtained results in this paper extend some well-known results for linear operator generalized inverses in this field.