Abstract
A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖s) is a Banach space, where ‖x‖s= max {‖x‖,‖-x‖} for all x∈X. 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).
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García-Raffi, L.M., Romaguera, S. & Sánchez-Pérez, E.A. The bicompletion of an asymmetric normed linear space. Acta Mathematica Hungarica 97, 183–191 (2002). https://doi.org/10.1023/A:1020823326919
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DOI: https://doi.org/10.1023/A:1020823326919