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

Journal of Numerical Analysis and Approximation Theory

Ş. Cobzaş¹  C. Mustăţa² 

[1] "Babeş-Bolyai" University, Cluj-Napoca, Romania;Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy;

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

DOI  :  

来源: DOAJ

【 摘 要 】

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 basedon 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.

【 授权许可】

Unknown