The m-generalized right group inverses in Banach algebras

2025/07/12 by Chen, Huanyin, Sheibani, Marjan
#15A09 #16U50 #16W10 #FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2507.10600

Abstract

In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the m-generalized right group decomposition and a polar-like property. Additionally, we present the representation of the m-generalized right group inverse using the generalized right core inverse, leading to new insights and properties for both the m-weak group inverse and the generalized group inverse.

Citations

• Generalized right group inverse in Banach *-algebras
• One-sided Drazin inverses in Banach algebras and perturbations of B-Fredholm spectra
• Group invertibility of the sum in rings and its applications
• m-weak group inverses in a ring with involution
• Weighted weak group inverse for Hilbert space operators
• Right core inverse and the related generalized inverses
• Weak group inverse
• Pseudo core inverses in rings with involution
• Pseudo core inverses in rings with involution

Related

• Generalized right group inverse in Banach *-algebras
• m-weak group inverse in a ring with proper involution
• m-weak group MP inverse
• On generalized inverses and Green's relations
• Common properties among various generalized inverses and constrained binary relations