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<p>Inspired by recently defined one-sided versions of generalized Drazin inverse, we consider some classes of Banach algebra elements. Basic properties and a number of characterizations for these elements are proposed. Consequently, many new characterizations for generalized <i>n</i>-strong Drazin invertibility are obtained. Furthermore, we characterize pseudo <i>n</i>-strongly Drazin invertible elements in the new manners.</p>

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New characterizations of generalized and pseudo n-strongly Drazin invertible elements

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Dijana Mosić,
  • Honglin Zou

摘要

Inspired by recently defined one-sided versions of generalized Drazin inverse, we consider some classes of Banach algebra elements. Basic properties and a number of characterizations for these elements are proposed. Consequently, many new characterizations for generalized n-strong Drazin invertibility are obtained. Furthermore, we characterize pseudo n-strongly Drazin invertible elements in the new manners.