A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

doi:10.1016/S0252-9602(17)30095-4

Abstract

Abstract:

In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in[12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

Key words: Banach space, bounded linear operator, metric projection, generalized inverse, perturbation analysis, Moore-Penrose, quasi-additive

Zi WANG, Yuwen WANG. A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2017, 37(6): 1619-1631.

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References

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