Extension of bounded linear functionals and best approximation in space with asymmetric norm

2 years ago

Approximation Theory, asymmetric norm, best approximation

Abstract

The present paper is concerned with the characterization of the elements of best approximation in a subspace $Y$ of a space with asymmetric norm, in terms of some linear functionals vanishing on $Y$ . The approach is based on some extension results, proved in Section 3, for bounded linear functionals on such spaces. Also, the well known formula for the distance to a hyperplane in a normed space is extended to the nonsymmetric case.

Authors

Ştefan Cobzaş
Babes-Bolyai University

Costica Mustata
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Romania

Keywords

Spaces with asymmetric norm; best approximation; Hahn-Banach theorem; characterization of best approximation.

Paper coordinates

C. Mustăţa and Şt. Cobzaş, Extension of bounded linear functionals and best approximation in space with asymmetric norm, Rev. Anal. Numer. Theor. Approx.. 33 (2004) no. 1, 39-50.

PDF

https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art5/Cobzas-Mustata-pdf

About this paper

Journal

Revue d’Analyse Numer. Theor. Approx.

Publisher Name

Publishing Romanian Academy

DOI

https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art5

Print ISSN

2457-6794

Online ISSN

2501-059X

google scholar link

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