, Volume 97, Issue 3, pp 183-191

The bicompletion of an asymmetric normed linear space

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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).