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.

Expressions for the G-Drazin Inverse of Additive Perturbed Elements

2011 ◽  
Vol 88-89 ◽  
pp. 509-514
Author(s):  
Li Guo ◽  
Yu Jing Liu
Keyword(s):  
Banach Algebra ◽  
Explicit Representation ◽  
Drazin Inverse ◽  
Generalized Drazin Inverse

To study the properties of the generalized Drazin inverse in a Banach algebra, an explicit representation of the generalized Drazin inverse under the some conditions. Thus some results are generalized.

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 Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5907-5917
Author(s):  
Daochang Zhang ◽  
Dijana Mosic
Keyword(s):  
Banach Algebra ◽  
Block Matrix ◽  
Drazin Inverse ◽  
Block Matrices ◽  
Explicit Formulae ◽  
Generalized Drazin Inverse

In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a 2x2 block matrix in a Banach algebra under weaker restrictions. Our results generalize and unify several results in the literature.

scholarly journals Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xiaoji Liu ◽  
Xiaolan Qin
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Block Matrix ◽  
Drazin Inverse ◽  
The Subject ◽  
Generalized Drazin Inverse

We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject.

scholarly journals Some Results on the Symmetric Representation of the Generalized Drazin Inverse in a Banach Algebra

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 105 ◽  
Author(s):  
Yonghui Qin ◽  
Xiaoji Liu ◽  
Julio Benítez
Keyword(s):  
Banach Algebra ◽  
Drazin Inverse ◽  
Symmetric Representation ◽  
Generalized Drazin Inverse

Based on the conditions a b 2 = 0 and b π ( a b ) ∈ A d , we derive that ( a b ) n , ( b a ) n , and a b + b a are all generalized Drazin invertible in a Banach algebra A , where n ∈ N and a and b are elements of A . By using these results, some results on the symmetry representations for the generalized Drazin inverse of a b + b a are given. We also consider that additive properties for the generalized Drazin inverse of the sum a + b .

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.

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