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arXiv · 2104.11862

Remark on common properties of the products $ac$ and $ba$

Yanxun Ren·Lining Jiang
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Abstract

In this paper, we discuss the common properties for the products $ac$ and $ba$ in various categories under the condition $a(ba)^{2}=abaca=acaba=(ac)^{2}a$. We prove that generalized Jacobson's lemma and Cline's formula are suitable for generalized n-strong Drazin invertible in rings, and generalized Jacobson's lemma is suitable for left and right Fredholm operator on Banach spaces.

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Yanxun Ren, Lining Jiang. 2021-04-24. Remark on common properties of the products $ac$ and $ba$. https://arxiv.org/abs/2104.11862

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