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

Marco Baronti; Vito Fragnelli; Grzegorz Lewicki

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 3, page 443-458
- ISSN: 0010-2628

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topBaronti, Marco, Fragnelli, Vito, and Lewicki, Grzegorz. "Extensions of linear operators from hyperplanes of $l^{(n)}_\infty $." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 443-458. <http://eudml.org/doc/247744>.

@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 -

## References

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