Core partial order for finite potent endomorphisms Diego Alba Alonso

• Diego Alba Alonso ^[1]
  1. [1] Universidad de Castilla-La Mancha

     Universidad de Castilla-La Mancha

     Ciudad Real, España

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 203-225
• Idioma: inglés
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• Resumen

  • The aim of this paper is to generalize the core inverse to arbitrary vector spaces using finite potent endomorphisms. As an application, the core partial order is studied in the set of finite potent endomorphisms (of index less than or equal to one), thus generalizing the theory of this order to infinite-dimensional vector spaces. Moreover, a pre-order is presented using the CN decomposition of a finite potent endomorphism. Finally, some questions concerning this pre-order are posed. Throughout the paper, some remarks are made in the framework of arbitrary Hilbert spaces using bounded finite potent endomorphisms.