Geodesic
Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 443-458.

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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.
Classification : 41A35, 41A52, 41A55, 41A65, 46A22, 47A20
Keywords: linear operator; extension of minimal norm; element of best approximation; strongly unique best approximation 
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     author = {Baronti, Marco and Fragnelli, Vito and Lewicki, Grzegorz},
     title = {Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {443--458},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1995},
     mrnumber = {1364484},
     zbl = {0831.41014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a4/}
}
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Baronti, Marco; Fragnelli, Vito; Lewicki, Grzegorz. Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 443-458. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a4/