6 papers
The higher order group inverse in a ring
Liu Dayong, Chen Huanyin
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring…
Additive results of group inverses in Banach algebras
Dayong Liu, Huanyin Chen
In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices…
Group invertibility of the sum in rings and its applications
Huanyin Chen, Dayong Liu, Marjan Sheibani
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inv…
Perturbation for group inverse in a Banach algebra
Dayong Liu, Tugce Pekacar Calci, Handan Kose +1
We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of is thereby given. These extend the ma…
The group invertibility of matrices over Bézout domains
Dayong Liu, Aixiang Fang
Let be a Bézout domain, and let with . If and are group invertible, we prove that is similar to . Moreover, we have $(AB)^{…
The Generalized Flanders' Theorem in Unit-regular Rings
Dayong Liu, Aixiang Fang
Let R be a unit-regular ring, and let a,b,c in R satisfy aba=aca. If ac and ba are group invertible, we prove that ac is similar to ba. Furthermore, if ac and ba are Drazin inverti…