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.
Highlights
Introduction and PreliminariesLet X and Y be Banach spaces, let T : X → Y be a mapping, and let D ⊂ X be a subset of X
The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel
Motivated by related work on A(T2,)S in the literature mentioned above and by our own recent research papers [13, 14], in this paper, we will establish the definition of the quasi-linear operator outer generalized inverse A(T2,Sh) with prescribed range T and kernel S
Summary
Let X and Y be Banach spaces, and let A : X → Y be a bounded linear operator. We first define and characterize the quasi-linear operator (resp., out) generalized inverse A(Th,)S (resp., A(T2,,Sh)) for the operator A, where T ⊂ X and S ⊂ Y are homogeneous subsets. We further investigate the perturbation problems of the generalized inverses A(Th,)S and A(T2,,Sh). The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel
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