Geodesic
Strong unicity criterion in some space of operators
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 81-87

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\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]).
Classification : 41A35, 41A50, 41A52, 41A65, 46B99
Keywords: best approximation; strongly unique best approximation; approximation in spaces of linear operators 
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     author = {Lewicki, Grzegorz},
     title = {Strong unicity criterion in some space of operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {81--87},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1993},
     mrnumber = {1240206},
     zbl = {0785.41023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a8/}
}
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Lewicki, Grzegorz. Strong unicity criterion in some space of operators. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 81-87. http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a8/