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

Ş. Cobzaş; C. Mustăţa

doi:10.33993/jnaat331-757

Authors

Ş. Cobzaş "Babeş-Bolyai" University, Cluj-Napoca, Romania
C. Mustăţa Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat331-757

Keywords:

spaces with asymmetric norm, best approximation, Hahn-Banach theorem, characterization of best approximation

Abstract views: 387

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.

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