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<p>In this paper, we introduce the concept of the <i>m</i>-generalized group inverse in a Banach *-algebra. This serves as a natural extension of the <i>m</i>-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the <i>m</i>-generalized group decomposition and a polar-like property. Additionally, we explore the relationships between the <i>m</i>-generalized group inverse and the generalized group inverse, leading to new properties for both the <i>m</i>-weak group inverse and the generalized group inverse.</p>

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On m-Generalized Group Inverse in Banach \(*\)-Algebras

  • 期刊论文

  • 发表日期：

    2025年2月27日

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  • Huanyin Chen

摘要

In this paper, we introduce the concept of the m-generalized group inverse in a Banach *-algebra. This serves as a natural extension of the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the m-generalized group decomposition and a polar-like property. Additionally, we explore the relationships between the m-generalized group inverse and the generalized group inverse, leading to new properties for both the m-weak group inverse and the generalized group inverse.