环和算子代数中广义\(n\) -强Drazin逆的Jacobson引理

Pub Date : 2022-06-28 DOI:10.3336/gm.57.1.01

Yanxun Ren, Lining Jiang

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引用次数: 1

摘要

本文将关于Drazin逆的Jacobson引理推广到环上的广义\(n\) -强Drazin逆，并证明\(1-ac\)是广义\(n\) -强Drazin可逆的当且仅当\(1-ba\)是广义\(n\) -强Drazin可逆，只要\(a(ba)^{2}=abaca=acaba=(ac)^{2}a\)。此外，还研究了左、右Fredholm算子的Jacobson引理，以及可逆性谱性质一致、Fredholm和指标谱性质一致的引理。

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

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.

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