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 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.

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 .

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.

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