LEFT AND RIGHT GENERALIZED DRAZIN INVERSES FOR CLOSED OPERATORS AND APPLICATION TO SINGULAR LINEAR EQUATIONS

被引：0

作者：

Messirdi, Sanaa ^{[1
]}

Messirdi, Sofiane ^{[2
,3
]}

Ayad-Djemai, Setti ^{[2
,3
]}

Messirdi, Bekkai ^{[3
,4
]}

机构：

[1] High Ind Inst Social Promot ISIPS, Hainut, Belgium

[2] Ahmed Ben Bella Univ Oran1, Fac Exact & Appl Sci, Dept Math, Oran, Algeria

[3] Lab Fundamental & Applicable Math Oran LMFAO, Oran, Algeria

[4] High Sch Elect & Energet Engn, Oran, Algeria

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2021年 / 51卷 / 01期

关键词：

left generalized Drazin inverse; right genaralized Drazin inverse; closed linear operator; GKD and SVEP; quasinilpotent perturbation; singular linear equation;

D O I：

10.1216/rmj.2021.51.225

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define and study left and right generalized Drazin inverses for a closed densely defined linear operator in a Hilbert space. These operators are characterized by means of the generalized Kato decomposition and the single-valued extension property. We prove that they are invariant under commuting quasinilpotent perturbations. Finally, we give an application to solve singular linear equations.

引用

页码：225 / 241

页数：17

共 18 条

[1] Aiena P., 2004, Fredholm and local spectral theory
[2] Benharrat Mohammed, 2019, Proyecciones (Antofagasta), V38, P897, DOI 10.22199/issn.0717-6279-2019-05-0058
[3] Campbell S. L., 1979, SURVEYS REFERENCE WO, V4
[4] Caradus S.R., 1978, QUEENS PAP PURE APPL, V50
[5] The σg-Drazin inverse and the generalized Mbekhta decomposition
Dajic, A.
Koliha, J. J.
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 57 (03) : 309 - 326
[6] Djellouli G., 2018, STIINT U CUZA IASI M, P221
[7] Gustafson K, 2000, STOCHASTIC PROCESSES, V29, P253
[8] Left and right generalized Drazin invertible operators
Hocine, Kouider Miloud
Benharrat, Mohammed
Messirdi, Bekkai
[J]. LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (08) : 1635 - 1648
[9] KATO T, PERTURBATION THEORY
[10] Khaldi N., 2017, MATH NOTES+, V101, P5

← 1 2 →