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Keywords:
linear operator; extension of minimal norm; element of best approximation; strongly unique best approximation
linear operator; extension of minimal norm; element of best approximation; strongly unique best approximation
Summary:
Let $Y \subset l^{(n)}_{\infty }$ be a hyperplane and let $A \in {\Cal L}(Y)$ be given. Denote $$ \align {\Cal A} = & \{L\in {\Cal L}(l^{(n)}_{\infty },Y):L\mid Y = A\} \text{ and} \ & \lambda_{A} = \inf \{\parallel L \parallel : L\in {\Cal A}\}. \endalign $$ In this paper the problem of calculating of the constant $\lambda_{A}$ is studied. We present a complete characterization of those $A \in {\Cal L}(Y)$ for which $\lambda_{A} = \parallel A \parallel $. Next we consider the case $\lambda_{A} > \parallel A \parallel $. Finally some computer examples will be presented.
References:
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