Generalized Drazin invertibility of the product and sum of two elements in a Banach algebra and its applications

Authors

HONGLIN ZOU
DIJANA MOSIC
JIANLONG CHEN

DOI

10.3906/mat-1605-8

Abstract

Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.

Keywords

Generalized Drazin inverse, Banach algebra, additive result, block matrix

First Page

548

Last Page

563

Recommended Citation

ZOU, HONGLIN; MOSIC, DIJANA; and CHEN, JIANLONG (2017) "Generalized Drazin invertibility of the product and sum of two elements in a Banach algebra and its applications," Turkish Journal of Mathematics: Vol. 41: No. 3, Article 8. https://doi.org/10.3906/mat-1605-8
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/8