• Quotient normed cones

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      https://www.ias.ac.in/article/fulltext/pmsc/116/02/0175-0191

    • Keywords

       

      Normed cone; extended quasi-metric; continuous linear mapping; bicompleteness; quotient cone; dual

    • Abstract

       

      Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖p,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)*, ¦¦ · ‖·‖p,p) can be identified as a distinguished subcone of the dual cone (X*, ¦¦ · ¦¦p, u). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.

    • Author Affiliations

       

      Oscar Valero1

      1. Departamento de Ciencias Matemáticas e Informática, Edificio Anselm Turmeda, Universidad de las Islas Baleares, Palma - 07122, Spain
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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