English

The $m$-generalized right group inverses in Banach algebras

Rings and Algebras 2025-07-16 v1 Functional Analysis

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.

Keywords

Cite

@article{arxiv.2507.10600,
  title  = {The $m$-generalized right group inverses in Banach algebras},
  author = {Huanyin Chen and Marjan Sheibani},
  journal= {arXiv preprint arXiv:2507.10600},
  year   = {2025}
}