The adjoint of an operator on a Banach space

• García-Pacheco, Francisco Javier ^[1]
  1. [1] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 823-840
• Idioma: inglés
• DOI: 10.1007/s13348-023-00414-8
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• Resumen

  • Self-adjoint operators in smooth Banach spaces have been already defined in recent works. Here, we extend the concept of adjoint of an operator to the scope of (non-necessarily Hilbert) Banach spaces, obtaining in particular the notion of self-adjoint operator in the non-smooth case. As a consequence, we define the probability density operator on Banach spaces and verify most of its well-known properties.