The Quasi-Linear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces
Jianbing Cao, Yifeng Xue · Journal of Operators · 2013
Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.