scholarly journals The weighted g-Drazin inverse for operators

2007 ◽  
Vol 82 (2) ◽  
pp. 163-181 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29 (1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

scholarly journals The Weighted g-drazin inverse for operators

2006 ◽  
Vol 81 (3) ◽  
pp. 405-423 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29(1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

scholarly journals A note on the perturbation bounds of W-weighted Drazin inverse of linear operator in Banach space

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 505-511 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Hai-Feng Ma ◽  
Marija Cvetkovic
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Perturbation Bound ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Perturbation Bounds ◽  
Weighted Drazin Inverse

We investigate the perturbation bound of the W-weighted Drazin inverse for bounded linear operators between Banach spaces and present two explicit expressions for the W-weighted Drazin inverse of bounded linear operators in Banach space, which extend the results in Chin. Anna. Math., 21C:1 (2000) 39-44 by Wei.

scholarly journals The Drazin inverse of the sum of two bounded linear operators and it’s applications

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2391-2402
Author(s):  
Hua Wang ◽  
Junjie Huang ◽  
Alatancang Chen
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear

Let P and Q be bounded linear operators on a Banach space. The existence of the Drazin inverse of P+Q is proved under some assumptions, and the representations of (P+Q)D are also given. The results recover the cases P2Q = 0,QPQ = 0 studied by Yang and Liu in [19] for matrices, Q2P = 0; PQP = 0 studied by Cvetkovic and Milovanovic in [7] for operators and P2Q + QPQ = 0, P3Q = 0 studied by Shakoor, Yang and Ali in [16] for matrices. As an application, we give representations for the Drazin inverse of the operator matrix A = (ACBD).

Weighted G-Drazin inverse for operators on Banach spaces

2019 ◽  
Vol 35 (2) ◽  
pp. 171-184 ◽  
Author(s):  
DIJANA MOSIC ◽  
Keyword(s):  
Banach Space ◽  
Partial Order ◽  
Banach Spaces ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear

We define an extension of weighted G-Drazin inverses of rectangular matrices to operators between two Banach spaces. Some properties of weighted G-Drazin inverses are generalized and some new ones are proved. Using weighted G-Drazin inverses, we introduce and characterize a new weighted pre-order on the set of all bounded linear operators between two Banach spaces. As an application, we present and study the G-Drazin inverse and the G-Drazin partial order for operators on Banach space.

scholarly journals Drazin inverse: representation, approximation, continuity and illustrations

2021 ◽  
Vol 13(62) (2) ◽  
pp. 463-478
Author(s):  
Sadli Bendjedid ◽  
Bekkai Messirdi ◽  
Sofiane Messirdi
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Iterative Processes ◽  
Inverse Representation

In this paper, we present some characteristics and expressions of the Drazin inverse for matrices and bounded linear operators in Banach spaces. We give a survey of some of results on the continuity of the Moore-Penrose and Drazin inverse, direct technics for computing the Drazin inverse are discussed, they are based on Euler-Knopp Method and characterized in terms of a limiting process. The examples presented are for illustrative purposes, some of which are provided for testing the considered iterative processes

Generalized Cline’s formula and common spectral property

2020 ◽  
pp. 2150094
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani Abdolyousefi
Keyword(s):  
Spectral Property ◽  
Banach Spaces ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

Let [Formula: see text] be an associative ring with an identity and suppose that [Formula: see text] satisfy [Formula: see text] If [Formula: see text] has generalized Drazin (respectively, p-Drazin, Drazin) inverse, we prove that [Formula: see text] has generalized Drazin (respectively, p-Drazin, Drazin) inverse. In particular, as applications, we obtain new common spectral property of bounded linear operators over Banach spaces.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

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