Further Results on the Generalized Drazin Inverse of Block Matrices in Banach Algebras

2014 ◽  
Vol 38 (2) ◽  
pp. 483-498 ◽  
Author(s):  
Milica Z. Kolundžija ◽  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Banach Algebras ◽  
Drazin Inverse ◽  
Block Matrices ◽  
Generalized Drazin Inverse

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 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 Formulas for the Drazin inverse of matrices over skew fields

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3377-3388 ◽  
Author(s):  
Lizhu Sun ◽  
Baodong Zheng ◽  
Shuyan Bai ◽  
Changjiang Bu
Keyword(s):  
Schur Complement ◽  
Drazin Inverse ◽  
Explicit Formulas ◽  
Block Matrices ◽  
Skew Fields ◽  
Generalized Drazin Inverse ◽  
Generalized Schur Complement ◽  
Appl Math

For two square matrices P and Q over skew fields, the explicit formulas for the Drazin inverse of P+Q are given in the cases of (i) PQ2=0, P2QP=0, (QP)2=0; (ii) P2QP=0, P3Q=0, Q2=0, which extend the results in [M.F. Mart?nez-Serrano et al., On the Drazin inverse of block matrices and generalized Schur complement, Appl. Math. Comput.] and [C. Deng et al., New additive results for the generalized Drazin inverse, J. Math. Anal. Appl.]. By using these formulas, the representations for the Drazin inverse of 2 x 2 block matrices over skew fields are obtained, which also extend some existing results.

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