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<p>The purpose of this paper is to introduce and study the class of generalized Saphar linear relations in Banach spaces. It is shown that these linear relations can be completely characterized in terms of an algebraic decomposition involving a Saphar linear relation and a bounded nilpotent operator. Other characterizations of these linear relations are also provided. Additionally, we examine two particular subclasses of generalized Saphar linear relations related to Drazin invertibility, namely the classes of left and right Drazin invertible linear relations.</p>

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On generalized Saphar linear relations

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Ayoub Ghorbel,
  • Melik Lajnef

摘要

The purpose of this paper is to introduce and study the class of generalized Saphar linear relations in Banach spaces. It is shown that these linear relations can be completely characterized in terms of an algebraic decomposition involving a Saphar linear relation and a bounded nilpotent operator. Other characterizations of these linear relations are also provided. Additionally, we examine two particular subclasses of generalized Saphar linear relations related to Drazin invertibility, namely the classes of left and right Drazin invertible linear relations.