Original scientific paper

https://doi.org/10.3336/gm.57.1.01

Jacobson's lemma for the generalized n-strong Drazin inverses in rings and in operator algebras

Yanxun Ren ; School of Mathematics and Statistics, Beijing Institute of Technology, 100081 Beijing, China
Lining Jiang ; School of Mathematics and Statistics, Beijing Institute of Technology, 100081 Beijing, China

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Abstract

In this paper, we extend Jacobson's lemma for Drazin inverses to the generalized \(n\)-strong Drazin inverses in a ring, and prove that \(1-ac\) is generalized \(n\)-strong Drazin invertible if and only if \(1-ba\) is generalized \(n\)-strong Drazin invertible, provided that \(a(ba)^{2}=abaca=acaba=(ac)^{2}a\). In addition, Jacobson's lemma for the left and right Fredholm operators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.

Keywords

Jacobson's lemma, generalized \(n\)-strong Drazin inverse, Fredholm operator, consistent in invertibility

Hrčak ID:

279728

URI

https://hrcak.srce.hr/279728

Publication date:

28.6.2022.

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