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 \(Y^{\perp}\) 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.
Authors
Costica Mustăţa
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academ, Romania
Keywords
Asymmetric normed spaces; extensions preserving asymmetric norm; best approximation
Paper coordinates
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.
About this paper
Journal
Revue d’Analyse Numerique et de Theorie de l’Approximation
Publisher Name
Publising Romanian Academy
DOI
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
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