Abstract: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 Theorem I.1.3 from [12] (see also [13]).
Keywords: best approximation, strongly unique best approximation, approximation in spaces of linear operators
AMS Subject Classification: Primary 41A65, 41A52, 41A35