Table of Contents
Journal of Operators
Volume 2013, Article ID 204587, 7 pages
http://dx.doi.org/10.1155/2013/204587
Research Article

The Quasi-Linear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, China
2Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 20 January 2013; Accepted 4 July 2013

Academic Editor: C. Morales

Copyright © 2013 Jianbing Cao and Yifeng Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.