COMMUTING PERTURBATIONS OF OPERATOR EQUATIONS

Xue Xu; Jiu Ding

doi:10.11948/20190382

2021 Volume 11 Issue 4

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Xue Xu, Jiu Ding. COMMUTING PERTURBATIONS OF OPERATOR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1691-1698. doi: 10.11948/20190382

Citation:

Xue Xu, Jiu Ding. COMMUTING PERTURBATIONS OF OPERATOR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1691-1698. doi: 10.11948/20190382

COMMUTING PERTURBATIONS OF OPERATOR EQUATIONS

Xue Xu¹,
Jiu Ding^2, ,

1.
Department of Mathematics, Harbin University, Harbin, Heilongjiang, 150001, China
2.
School of Mathematics and Natural Sciences, The University of Southern Mississippi, Hattiesburg, MS 39406, USA

Corresponding author: Email: jiuding@gmail.com(J. Ding)
Fund Project: The research of Xue Xu was partially supported by NSFH(No. LH2020A002) and HUDF(No. 2019101)

Abstract

Abstract

Let $X$ be a Banach space and let $T : X \rightarrow X$ be a bounded linear operator with closed range. We study a class of commuting perturbations of the corresponding operator equation, using the concept of the spectral radius of a bounded linear operator. Our results extend the classic perturbation theorem for invertible operators and its generalization for arbitrary operators under the commutability assumption.
- Operator equation /
- generalized inverse /
- commuting perturbation /
- spectral radius /
- projection /
- least squares
MSC: 15A18

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References

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