The Properties of the Generalized G-zhou Inverses and the Generalization of the Weighted Generalized Inverses Based on the W* Operator
Xingsong Yang, Weize Gao · Journal of Physics Conference Series · 2025
Abstract In this paper, we have investigated the generalized inverse form of a class of elements in a ring, and propose a new generalized inverses generalized G-zhou inverses. An element a ∈ R is called generalized G-zhou invertible if there exists an element x ∈ R such that x ∈ comm 2 (a), xax = x, and an + a n+1 f (a) – ab ∈ Rqnil . And fulfill any x ∈ R, (1 + af (a)) x ∈ Rqnil ⇔ x ∈ Rqnil . A few fundamental characteristics of the inverse are examined. For the inverse, we demonstrate expansions of Clines formula. We prove the generality of the generalized G-zhou inverse, which is a more general definition without the generalized inverse itself and an equivalent proof. Weighted Mosic-Abyzov inverses and Weight zhou inverses are defined and characterized in a Banach algebra. The equivalence of the w* operator on Banach algebras and ordinary operations is studied.