Strong unicity criterion in some space of operators
Lewicki, Grzegorz
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 81-87 / Harvested from Czech Digital Mathematics Library
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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]).

Publié le : 1993-01-01
Classification:  41A35,  41A50,  41A52,  41A65,  46B99 
@article{118558,
     author = {Grzegorz Lewicki},
     title = {Strong unicity criterion in some space of operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {81-87},
     zbl = {0785.41023},
     mrnumber = {1240206},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118558}
}

Lewicki, Grzegorz. Strong unicity criterion in some space of operators. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 81-87. http://gdmltest.u-ga.fr/item/118558/

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