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math.RA2020
Generalized Zhou inverses in rings
Huanyin Chen, Marjan Sheibani Abdolyousefi
We introduce and study a new class of generalized inverses in rings. An element in a ring has generalized Zhou inverse if there exists such that $bab=b, b\in comm^…
math.RA2020
Generalized Jacobson's lemma in a Banach algebra
Huanyin Chen, Marjan Sheibani Abdolyousefi
Let A be a Banach algebra, and let a; b; c 2 A satisfying a(ba)^2 = abaca = acaba = (ac)^2a: We prove that 1 - ba\in A^d if and only if 1 - ac \in A^d. In this case, (1-ac)^d =1-a(…
math.RA2020
Generalized Cline's formula for G-Drazin inverse in a ring
Huanyin Chen, Marjan Sheibani Abdolyousefi
In this paper, we give a generalized Cline's formula for the generalized Drazin inverse. Let be a ring, and let satisfying $$\begin{array}{c} (ac)^2 = (db)(ac),…