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

2 years ago

(original), Approximation Theory, asymmetric norm, paper

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 asymmetricnorm; 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.

PDF

https://ictp.acad.ro/jnaat/journal/article/view/2003-vol32-no2-art7/Mustata-pdf??

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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