Marco Baronti, Vito Fragnelli, Grzegorz Lewicki
Extensions of linear operators from hyperplanes of $l^{(n)}_{\infty }$

Comment.Math.Univ.Carolinae 36,3 (1995) 443-458.

Abstract:Let $Y \subset l^{(n)}_{\infty }$ be a hyperplane and let $A \in {\Cal L}(Y)$ be given. Denote $$ \align {\Cal A} = & \{L\in {\Cal L}(l^{(n)}_{\infty },Y):L | Y = A\} \text { and} & \lambda _{A} = \inf \{||L ||: L\in {\Cal A}\}. \endalign $$ 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 $\lambda _{A} = ||A ||$. Next we consider the case $\lambda _{A} > ||A ||$. Finally some computer examples will be presented.

Keywords: linear operator, extension of minimal norm, element of best approximation, strongly unique best approximation
AMS Subject Classification: 41A35, 41A52, 41A65, 41A55