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

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.

the proof of theorem is incorrect

Cited by in corpus (1)

• Generalized Cline's formula and Jacobson's lemma in a ring