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Keywords:
best approximation; strongly unique best approximation; approximation in spaces of linear operators
best approximation; strongly unique best approximation; approximation in spaces of linear operators
Summary:
\font\muj=rsfs10 \font\mmuj=rsfs8 Let $X$ be a finite dimensional Banach space and let $Y\subset X$ be a hyperplane. Let $\text{\mmuj L}\,_Y=\{L\in \text{\mmuj L}\,(X,Y):L\mid _Y=0\}$. In this note, we present sufficient and necessary conditions on $L_0\in \text{\mmuj L}\,_Y$ being a strongly unique best approximation for given $L\in \text{\mmuj L}\,(X)$. Next we apply this characterization to the case of $X=l_\infty ^n$ and to generalization of \linebreak Theorem I.1.3 from [12] (see also [13]).
References:
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