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<p>We prove a new formula for the generalized Drazin inverse of a sum in a Banach algebra. As an application, we derive new representations for the generalized Drazin inverse of block operator matrices. These results extend the main results of Mosić (Bull. Malays. Sci. Soc., 40 (2017), 1465–1478) to a broader setting.</p>

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A new formula for the generalized Drazin inverse in Banach algebras

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Huanyin Chen,
  • Marjan Sheibani

摘要

We prove a new formula for the generalized Drazin inverse of a sum in a Banach algebra. As an application, we derive new representations for the generalized Drazin inverse of block operator matrices. These results extend the main results of Mosić (Bull. Malays. Sci. Soc., 40 (2017), 1465–1478) to a broader setting.