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

Abstract EN

Let X and Y be Banach spaces, and let A:X→Y be a bounded linear operator.

In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse AT,S(h) (resp., AT,S(2,h)) for the operator A, where T⊂X and S⊂Y are homogeneous subsets.

Then, we further investigate the perturbation problems of the generalized inverses AT,S(h) and AT,S(2,h).

The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.