Acta Mathematica Hungarica

, Volume 97, Issue 3, pp 183–191 | Cite as

The bicompletion of an asymmetric normed linear space

  • L. M. García-Raffi
  • S. Romaguera
  • E. A. Sánchez-Pérez
Article

Abstract

A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖s) is a Banach space, where ‖xs= max {‖x‖,‖-x‖} for all xX. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖Y). Furthermore the space (Y,‖·‖Y) is unique (up to isometric isomorphism).

isometric isomorphism biBanach space asymmetric normed linear space bicompletion 

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Copyright information

© Kluwer Academic Publishers/Akadémiai Kiadó 2002

Authors and Affiliations

  • L. M. García-Raffi
    • 1
  • S. Romaguera
    • 1
  • E. A. Sánchez-Pérez
    • 1
  1. 1.Escuela de Caminos Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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