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

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Ş. Cobzaş C. Mustăţa


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