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arXiv · 1904.11982

Generalized Cline's Formula for G-Drazin Inverse

Huanyin Chen·Marjan Sheibani Abdolyousefi
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Abstract

Let $R$ be an associative ring with an identity and suppose that $a,b,c,d \in R$ satisfy $bdb = bac,dbd = acd$. If $ac$ has generalized Drazin ( respectively, pseudo Drazin, Drazin) inverse, we prove that $bd$ has generalized Drazin (respectively, pseudo Drazin, Drazin) inverse. In particular, as applications, we obtain new common spectral properties of bounded linear operators over Banach spaces.

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BibTeXRIS

Huanyin Chen, Marjan Sheibani Abdolyousefi. 2019-04-26. Generalized Cline's Formula for G-Drazin Inverse. https://arxiv.org/abs/1904.11982

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