Extensions of linear operators from hyperplanes of $l_{\infty }^{\left(n\right)}$

@article{Baronti1995,
abstract = {Let $Y \subset l^\{(n)\}_\{\infty \}$ be a hyperplane and let $A \in \{\mathcal \{L\}\}(Y)$ be given. Denote \[ \begin\{@align\}\{1\}\{-1\}\{\mathcal \{A\}\} = & \lbrace L\in \{\mathcal \{L\}\}(l^\{(n)\}\_\{\infty \},Y):L\mid Y = A\rbrace \text\{ and\} \ & \lambda \_\{A\} = \inf \lbrace \parallel L \parallel : L\in \{\mathcal \{A\}\}\rbrace . \end\{@align\}\] In this paper the problem of calculating of the constant $\lambda _\{A\}$ is studied. We present a complete characterization of those $A \in \{\mathcal \{L\}\}(Y)$ for which $\lambda _\{A\} = \parallel A \parallel $. Next we consider the case $\lambda _\{A\} > \parallel A \parallel $. Finally some computer examples will be presented.},
author = {Baronti, Marco, Fragnelli, Vito, Lewicki, Grzegorz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear operator; extension of minimal norm; element of best approximation; strongly unique best approximation},
language = {eng},
number = {3},
pages = {443-458},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extensions of linear operators from hyperplanes of $l^\{(n)\}_\infty $},
url = {http://eudml.org/doc/247744},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Baronti, Marco
AU - Fragnelli, Vito
AU - Lewicki, Grzegorz
TI - Extensions of linear operators from hyperplanes of $l^{(n)}_\infty $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 443
EP - 458
AB - Let $Y \subset l^{(n)}_{\infty }$ be a hyperplane and let $A \in {\mathcal {L}}(Y)$ be given. Denote \[ \begin{@align}{1}{-1}{\mathcal {A}} = & \lbrace L\in {\mathcal {L}}(l^{(n)}_{\infty },Y):L\mid Y = A\rbrace \text{ and} \ & \lambda _{A} = \inf \lbrace \parallel L \parallel : L\in {\mathcal {A}}\rbrace . \end{@align}\] In this paper the problem of calculating of the constant $\lambda _{A}$ is studied. We present a complete characterization of those $A \in {\mathcal {L}}(Y)$ for which $\lambda _{A} = \parallel A \parallel $. Next we consider the case $\lambda _{A} > \parallel A \parallel $. Finally some computer examples will be presented.
LA - eng
KW - linear operator; extension of minimal norm; element of best approximation; strongly unique best approximation
UR - http://eudml.org/doc/247744
ER -