The Quasi-Linear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces. (4th August 2013) - Cao, Jianbing; Xue, Yifeng
Abstract : LetX andY be Banach spaces, and letA : X → Y be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverseA T, S ( h ) (resp., A T, S ( 2, h ) ) for the operatorA, whereT ⊂ X andS ⊂ Y are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inversesA T, S ( h ) andA T, S ( 2, h ) . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.