# Generalized Jacobson’s lemma for generalized Drazin inverses

@article{Chen2021GeneralizedJL, title={Generalized Jacobson’s lemma for generalized Drazin inverses}, author={Huanyin Chen and Marjan Sheibani}, journal={Filomat}, year={2021} }

We present new generalized Jacobson?s lemma for generalized Drazin inverses.
This extends the main results on g-Drazin inverse of Yan, Zeng and Zhu
(Linear & Multilinear Algebra, 68(2020), 81-93).

## References

SHOWING 1-10 OF 15 REFERENCES

### Generalized Jacobson's lemma for Drazin inverses and its applications

- MathematicsLinear and Multilinear Algebra
- 2018

ABSTRACT Let R be any associative ring with unit 1 and suppose that satisfy we prove that 1−ac is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible if and only if 1−bd is Drazin…

### GENERALIZED INVERSES OF A SUM IN RINGS

- MathematicsBulletin of the Australian Mathematical Society
- 2010

Abstract We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1−ba in terms of generalized inverses of 1−ab. In our…

### New extensions of Cline's formula for generalized inverses

- Mathematics
- 2017

In this paper, Cline's formula for the well-known generalized inverses such as Drazin inverse, pseudo Drazin inverse and generalized Drazin inverse is extended to the case when $\left\{…

### Extensions of Jacobson's Lemma

- Mathematics
- 2013

Jacobson's Lemma, relating different kinds of non singularity of ca − 1 and ac − 1, extends to ba − 1 whenever aca = aba.

### Weak inverses of products — Cline’s formula meets Jacobson lemma

- Mathematics
- 2017

We study extensions of Cline’s formula and Jacobson lemma for one-sided, commuting and bicommuting weak inverses, in semigroups and general rings. In particular, we provide various isomorphisms…

### A generalized Drazin inverse

- MathematicsGlasgow Mathematical Journal
- 1996

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…

### On Drazin Spectral Equation for the Operator Products

- Mathematics
- 2020

Let X be a Banach space and A , B , C , D be bounded linear operators on X . In this paper we show that the Drazin (resp. generalized Drazin) spectrum of AC coincides with the Drazin (resp.…

### Extensions of Jacobson’s lemma for Drazin inverses

- Mathematics
- 2017

We study the generalization of Jacobson’s lemma for the group inverse, Drazin inverse, generalized Drazin inverse and pseudo Drazin inverse of $$1-bd$$1-bd (or $$1-ac$$1-ac) in a ring when…