scholarly journals Representations for generalized Drazin inverse of operator matrices over a Banach space

2016 ◽  
Vol 40 ◽  
pp. 428-437
Author(s):  
Daochang ZHANG
Keyword(s):  
Banach Space ◽  
Drazin Inverse ◽  
Operator Matrices ◽  
Generalized Drazin Inverse

On the Generalized Drazin Inverse of the Sum of Two Operators

2013 ◽  
Vol 846-847 ◽  
pp. 1286-1290
Author(s):  
Shi Qiang Wang ◽  
Li Guo ◽  
Lei Zhang
Keyword(s):  
Banach Space ◽  
Explicit Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Generalized Drazin Inverse

In this paper, we investigate additive properties for the generalized Drazin inverse of bounded linear operators on Banach space . We give explicit representation of the generalized Drazin inverse in terms of under some conditions.

scholarly journals New extensions of Cline’s formula for generalized inverses

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1973-1980 ◽  
Author(s):  
Qingping Zeng ◽  
Zhenying Wu ◽  
Yongxian Wen
Keyword(s):  
Banach Space ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Space Operator ◽  
Cline’S Formula ◽  
Generalized Drazin Inverse

In this paper, Cline?s formula for the well-known generalized inverses such as Drazin inverse, pseudo Drazin inverse and generalized Drazin inverse is extended to the case when ( acd = dbd dba = aca. Also, applications are given to some interesting Banach space operator properties like algebraic, meromorphic, polaroidness and B-Fredholmness.

scholarly journals Expressions for the g-Drazin inverse in a Banach algebra

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3845-3854
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani
Keyword(s):  
Banach Algebra ◽  
Complex Number ◽  
Block Matrix ◽  
Explicit Representation ◽  
Drazin Inverse ◽  
Operator Matrices ◽  
Nonzero Complex Number ◽  
Generalized Drazin Inverse

We explore the generalized Drazin inverse in a Banach algebra. Let A be a Banach algebra, and let a,b ? Ad. If ab = ?a?bab? for a nonzero complex number ?, then a + b ? Ad. The explicit representation of (a + b)d is presented. As applications of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. The main results of Liu and Qin [Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices, Sci. World J., 2015, 156934.8] are extended.

Some results on the generalized Drazin inverse of operator matrices

2009 ◽  
Vol 58 (4) ◽  
pp. 503-521 ◽  
Author(s):  
Chunyuan Deng ◽  
Dragana S. Cvetković-Ilić ◽  
Yimin Wei
Keyword(s):  
Drazin Inverse ◽  
Operator Matrices ◽  
Generalized Drazin Inverse

scholarly journals Additive results for the generalized Drazin inverse

2002 ◽  
Vol 73 (1) ◽  
pp. 115-126 ◽  
Author(s):  
Dragan S. Djordjević ◽  
Yimin Wei
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Drazin Inverse ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Special Cases ◽  
Arbitrary Complex ◽  
Additive Perturbation ◽  
Generalized Drazin Inverse ◽  
Banach Space Operators

AbstractAdditive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad denotes the generalized Drazin inverse of a bounded linear operator A on an arbitrary complex Banach space, then in some special cases (A + B)d is computed in terms of Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

scholarly journals The perturbation theory for the Drazin inverse and its applications II

2001 ◽  
Vol 70 (2) ◽  
pp. 189-198 ◽  
Author(s):  
Vladimir Rakočevič ◽  
Yimin Wei
Keyword(s):  
Banach Space ◽  
Perturbation Theory ◽  
Banach Algebras ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Generalized Drazin Inverse

AbstractWe study the perturbation of the generalized Drazin inverse for the elements of Banach algebras and bounded linear operators on Banach space. This work, among other things, extends the results obtained by the second author and Guorong Wang on the Drazin inverse for matrices.

scholarly journals A generalized Drazin inverse

1996 ◽  
Vol 38 (3) ◽  
pp. 367-381 ◽  
Author(s):  
J. J. Koliha
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Algebra ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Main Theme ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Spectral Point ◽  
Generalized Drazin Inverse

The main theme of this paper can be described as a study of the Drazin inverse for bounded linear operators in a Banach space X when 0 is an isolated spectral point ofthe operator. This inverse is useful for instance in the solution of differential equations formulated in a Banach space X. Since the elements of X rarely enter into our considerations, the exposition seems to gain in clarity when the operators are regarded as elements of the Banach algebra L(X).

scholarly journals Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaoji Liu ◽  
Xiaolan Qin
Keyword(s):  
Banach Algebra ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Operator Matrices ◽  
Generalized Drazin Inverse ◽  
Explicit Expressions

We investigate additive properties of the generalized Drazin inverse in a Banach algebraA. We find explicit expressions for the generalized Drazin inverse of the suma+b, under new conditions ona,b∈A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

scholarly journals Perturbation bound for the generalized Drazin inverse of an operator in Banach space

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5177-5191 ◽  
Author(s):  
Xiaoji Liu ◽  
Yonghui Qin
Keyword(s):  
Banach Space ◽  
Perturbation Analysis ◽  
Upper Bound ◽  
Drazin Inverse ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Perturbation Bound ◽  
Generalized Drazin Inverse ◽  
Necessary And Sufficient

In this paper, we consider perturbation analysis for the generalized Drazin inverse of an operator in Banach space. An necessary and sufficient condition for the generalized Drazin invertible is given. The upper bound is given under some certain conditions, and a relative perturbation bound is also considered.

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