Publication date: 30 June 2022
Volume: Vol 57
Issue: Svezak 1
Pages: 1-15
DOI: https://doi.org/10.3336/gm.57.1.01
Izvorni znanstveni članak
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
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.
279728
28.6.2022.
Posjeta: 450 *