JACOBSON’S LEMMA FOR THE GENERALIZED n-STRONG DRAZIN INVERSES IN RINGS AND IN OPERATOR ALGEBRAS

Yanxun Ren; Lining Jiang

doi:10.3336/gm.57.1.01

JACOBSON’S LEMMA FOR THE GENERALIZED n-STRONG DRAZIN INVERSES IN RINGS AND IN OPERATOR ALGEBRAS

Yanxun Ren, Lining Jiang

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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)²a. In addition, Jacobson’s lemma for the left and right Fredholm op-erators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Glasnik Matematicki
Volume	57
Issue number	1
DOIs	https://doi.org/10.3336/gm.57.1.01
Publication status	Published - 28 Jun 2022

Keywords

Fredholm operator
Jacobson’s lemma
consistent in invertibility
generalized n-strong Drazin inverse

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abstract = "In this paper, we extend Jacobson{\textquoteright}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)2a. In addition, Jacobson{\textquoteright}s lemma for the left and right Fredholm op-erators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.",

keywords = "Fredholm operator, Jacobson{\textquoteright}s lemma, consistent in invertibility, generalized n-strong Drazin inverse",

author = "Yanxun Ren and Lining Jiang",

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N2 - 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)2a. In addition, Jacobson’s lemma for the left and right Fredholm op-erators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.

AB - 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)2a. In addition, Jacobson’s lemma for the left and right Fredholm op-erators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.

KW - Fredholm operator

KW - Jacobson’s lemma

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ER -

JACOBSON’S LEMMA FOR THE GENERALIZED n-STRONG DRAZIN INVERSES IN RINGS AND IN OPERATOR ALGEBRAS

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Keywords

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