Scholarlink

<p>We extend the concept of generalized Drazin-Riesz inverse for operators using a generalized Drazin-Riesz invertible operator rather than a Riesz operator in the definition of generalized Drazin-Riesz inverse. Many characterizations of extended generalized Drazin-Riesz invertible operator are verified in terms of idempotents, tripotents and powers. We prove that extended generalized Drazin-Riesz invertibility is equivalent to generalized Drazin-Riesz invertibility. Thus, we consequently get new characterizations for generalized Drazin-Riesz invertibility. An extension of Cline’s formula for extended generalized Drazin-Riesz inverse is considered. Also, we present and characterize one-sided extended generalized Drazin-Riesz inverses as extensions of one-sided generalized Drazin-Riesz inverses.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Extensions of generalized Drazin-Riesz inverses

  • 期刊论文

  • 发表日期：

    2026年4月21日

查看全文
  • Dijana Mosić,
  • Fernando Pablos Romo

摘要

We extend the concept of generalized Drazin-Riesz inverse for operators using a generalized Drazin-Riesz invertible operator rather than a Riesz operator in the definition of generalized Drazin-Riesz inverse. Many characterizations of extended generalized Drazin-Riesz invertible operator are verified in terms of idempotents, tripotents and powers. We prove that extended generalized Drazin-Riesz invertibility is equivalent to generalized Drazin-Riesz invertibility. Thus, we consequently get new characterizations for generalized Drazin-Riesz invertibility. An extension of Cline’s formula for extended generalized Drazin-Riesz inverse is considered. Also, we present and characterize one-sided extended generalized Drazin-Riesz inverses as extensions of one-sided generalized Drazin-Riesz inverses.