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


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 \(Y^{\perp}\) 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.


Costica Mustăţa
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academ, Romania


Asymmetric normed spaces; extensions preserving asymmetricnorm; best approximation

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C. Mustăţa, On the uniqueness of extension and unique best approximation in the dual of an asymmetric normed linear space, Rev. Anal. Numer. Theor. Approx. 32 (2003) no. 2, 187-192.


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Revue d’Analyse Numerique et de Theorie de l’Approximation

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