Additive results for the Drazin inverse of block matrices and applications

Ljubisavljevic, Jelena; Cvetković-Ilić, Dragana S.

doi:10.1016/j.cam.2011.02.029

Cited by 30 publications

(11 citation statements)

References 9 publications

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“…Djordjevic and Wei [7] generalized the result of [25] to bounded linear operators on an arbitrary complex Banach space. More results on generalized Drazin inverse can be found in [6,8,29,30,35]. In Section 4, we give a new additive result of the generalized Drazin inverse for two bounded linear operators P, Q ∈ B(X) with P Q d = 0 and P Q i P = 0, for any integer i ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

The generalized Drazin inverse of operator matrices

Guo¹,

Zou

Chen

2020

Hacettepe Journal of Mathematics and Statistics

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Representations for the generalized Drazin inverse of an operator matrix A B C D are presented in terms of A, B, C, D and the generalized Drazin inverses of A, D, under the condition that BD d = 0, and BD i C = 0, for any nonnegative integer i. Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators P, Q ∈ B(X) with P Q d = 0 and P Q i P = 0, for any integer i ≥ 1. As corollaries, several well-known results are generalized.

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Section: Introductionmentioning

confidence: 99%

The generalized Drazin inverse of operator matrices

Guo¹,

Zou

Chen

2020

Hacettepe Journal of Mathematics and Statistics

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“…Moreover, when Ind(A) ≤ 1, the matrix X is known as the group inverse and noticed by A [1] . More on Drazin inverses and generalized Drazin inverses see in [10,17]. For two complementary subspaces L, M ∈ C n , that satisfy L M = C n .…”

Section: Introductionmentioning

confidence: 99%

The new revisitation of core EP inverse of matrices

Zheng

Jie

2019

Filomat

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In this paper, we study some properties of core-EP inverse of square matrices. Firstly, we extend the obtained theorem proved by K.M. Prasad and K.S. Mohana. Then some properties of core-EP inverse have been given, through applying the conditions (AX) * = AX, XA k+1 = A k and R(X) = R(X *) = R(A k). Secondly, we get some characterizations of core-EP inverse by employing the conditions AX = P A k and XA = P R(A k),N((A k+1) * A). Finally, we get some properties of core-EP inverse by utilizing the condition A k+1 X = A k P A k. (i) XAX = X, (ii) XA = AX, (iii) XA k+1 = A k , for some positive integer k, 2010 Mathematics Subject Classification. 15A09 Keywords. core-EP inverse, core-EP decomposition of matrices, core inverse, the orthogonal projection of matrices.

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“…For bounded linear operators, the Drazin inverse was introduced and studied by Caradus [2]. It is shown that the Drazin inverse has proved helpful in analyzing Markov chains, difference equation, differential equations, Cauchy problems and iterative procedures [1,3,11,13,14]. Now, we recall some definitions and basic fact about the Drazin inverse.…”

Section: Introductionmentioning

confidence: 99%

On linear operators for which TTD is normal

Yousefi

Dana

2019

Filomat

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A Drazin invertible operator T ∈ B(H) is called skew D-quasi-normal operator if T * and TT D commute or equivalently TT D is normal. In this paper, firstly we give a list of conditions on an operator T, each of which is equivalent to T being skew D-quasi-normal. Furthermore, we obtain the matrix representation of these operators. We also develop some basic properties of such operators. Secondly we extend the Kaplansky theorem and the Fuglede-Putnam commutativity theorem for normal operators to skew D-quasi-normal matrices.

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Additive results for the Drazin inverse of block matrices and applications

Cited by 30 publications

References 9 publications

The generalized Drazin inverse of operator matrices

The generalized Drazin inverse of operator matrices

The new revisitation of core EP inverse of matrices

On linear operators for which TTD is normal

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