Antiproximinal sets in the Banach space c ( X )

S. Cobzaş

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 247-253
  • ISSN: 0010-2628

Abstract

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If X is a Banach space then the Banach space c ( X ) of all X -valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C ( X ) ∖ V has a nearest point in V .

How to cite

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Cobzaş, S.. "Antiproximinal sets in the Banach space $c(X)$." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 247-253. <http://eudml.org/doc/248056>.

@article{Cobzaş1997,
abstract = {If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C(X)\setminus V$ has a nearest point in $V$.},
author = {Cobzaş, S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {antiproximinal sets; best approximation; antiproximinal sets; best approximation},
language = {eng},
number = {2},
pages = {247-253},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Antiproximinal sets in the Banach space $c(X)$},
url = {http://eudml.org/doc/248056},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Cobzaş, S.
TI - Antiproximinal sets in the Banach space $c(X)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 247
EP - 253
AB - If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C(X)\setminus V$ has a nearest point in $V$.
LA - eng
KW - antiproximinal sets; best approximation; antiproximinal sets; best approximation
UR - http://eudml.org/doc/248056
ER -

References

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  14. Phelps R.R., Subreflexive normed linear spaces, Archiv der Math. 8 (1957), 444-450. (1957) MR0099588
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  20. Werner D., Funktionalanalysis, Springer Verlag, Berlin-Heidelberg-New York, 1995. Zbl1161.46001MR1787146

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