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<p>This paper proposes and investigates the core inverse and dual core inverse of bounded closed linear relations defined everywhere. The concept of the core invertible is extended to linear relation case first, and the uniqueness of the core inverse is further proved. Then, through appropriate selections of some space decompositions, a condition for a linear relation to be core invertible is obtained, and some representations and properties of the core inverse of linear relations are presented. Additionally, the analogues concerning the dual core inverse of linear relations are also given. This paper recovers some of the results of O. M. Baksalary and G. Trenkler (Core inverse of matrices. Linear and Multilinear Algebra 58(6), 681–69, 2010) for matrices and Rakić, et al. (Core inverse and core partial order of Hilbert space operators. Appl. Math. Comput. 244, 283–302, 2014) for Hilbert space operators.</p>

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Core Inverse of Linear Relations

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Jianchao Sun,
  • Qiang Zhang,
  • JunJie Huang

摘要

This paper proposes and investigates the core inverse and dual core inverse of bounded closed linear relations defined everywhere. The concept of the core invertible is extended to linear relation case first, and the uniqueness of the core inverse is further proved. Then, through appropriate selections of some space decompositions, a condition for a linear relation to be core invertible is obtained, and some representations and properties of the core inverse of linear relations are presented. Additionally, the analogues concerning the dual core inverse of linear relations are also given. This paper recovers some of the results of O. M. Baksalary and G. Trenkler (Core inverse of matrices. Linear and Multilinear Algebra 58(6), 681–69, 2010) for matrices and Rakić, et al. (Core inverse and core partial order of Hilbert space operators. Appl. Math. Comput. 244, 283–302, 2014) for Hilbert space operators.