On the uniqueness of extension and unique best approximation in the dual of an asymmetric normed linear space

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Costică Mustăţa

Abstract

A well known result of R. R. Phelps (1960) asserts that in order that every linear continuous functional, defined on a subspace \(Y\) of a real normed space \(X\), have a unique norm preserving extension it is necessary and sufficient that its annihilator \(Y^\bot\) be a Chebyshevian subspace of \(X^\ast\). The aim of this note is to show that this result holds also in the case of spaces with asymmetric norm.

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Keywords
asymmetric normed spaces; extensions preserving asymmetric norm; best approximation
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