Generalized group inverse in Banach *-algebras
Huanyin Chen, Marjan Sheibani · Research Square · 2023
Abstract In this paper, we introduce the notion of the generalized group inverse in a *-Banach algebra. This is a natural generalization of weak group inverse for a complex matrix and bounded linear operator over a Hilbert space. We present polar-like property for the generalized group inverse and characterize it by the generalized Drazin inverse. Furthermore, the relations between generalized group inverse and generalized core-EP inverse are investigated. 2020 Mathematics Subject Classification. 15A09, 16U90, 46H05.