Representations for the Generalized Drazin Inverse of Bounded Linear Operators

2010 ◽  
pp. 423-430
Author(s):  
Li Guo ◽  
Xiankun Du
Keyword(s):  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
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 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).

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.

Common spectral properties of linear operators A and B satisfying AkBkAk = Ak+1 and BkAkBk = Bk+1

2019 ◽  
Vol 12 (05) ◽  
pp. 1950084
Author(s):  
Anuradha Gupta ◽  
Ankit Kumar
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Spectral Properties ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

Let [Formula: see text] and [Formula: see text] be two bounded linear operators on a Banach space [Formula: see text] and [Formula: see text] be a positive integer such that [Formula: see text] and [Formula: see text], then [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] have some common spectral properties. Drazin invertibility and polaroidness of these operators are also discussed. Cline’s formula for Drazin inverse in a ring with identity is also studied under the assumption that [Formula: see text] for some positive integer [Formula: see text].

scholarly journals Generalized cline’s formula for g-Drazin inverse in a ring

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2573-2583
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Banach Algebra ◽  
Spectral Property ◽  
Banach Spaces ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear ◽  
Group Inverses ◽  
Cline’S Formula ◽  
Generalized Drazin Inverse ◽  
Weaker Conditions

In this paper, we give a generalized Cline?s formula for the generalized Drazin inverse. Let R be a ring, and let a, b, c, d ? R satisfying (ac)2 = (db)(ac), (db)2 = (ac)(db), b(ac)a = b(db)a, c(ac)d = c(db)d. Then ac ? Rd if and only if bd ? Rd. In this case, (bd)d = b((ac)d)2d: We also present generalized Cline?s formulas for Drazin and group inverses. Some weaker conditions in a Banach algebra are also investigated. These extend the main results of Cline?s formula on g-Drazin inverse of Liao, Chen and Cui (Bull. Malays. Math. Soc., 37(2014), 37-42), Lian and Zeng (Turk. J. Math., 40(2016), 161-165) and Miller and Zguitti (Rend. Circ. Mat. Palermo, II. Ser., 67(2018), 105-114). As an application, new common spectral property of bounded linear operators over Banach spaces is obtained.

Additive Results of the Drazin Inverse for Bounded Linear Operators

2013 ◽  
Vol 8 (1) ◽  
pp. 349-358 ◽  
Author(s):  
Junjie Huang ◽  
Yunfeng Shi ◽  
Alatancang Chen
Keyword(s):  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear

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).

Sign in / Sign up

Export Citation Format

Share Document