Chebyshev centers in hyperplanes of
Czechoslovak Mathematical Journal (2002)
- Volume: 52, Issue: 4, page 721-729
- ISSN: 0011-4642
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topVeselý, Libor. "Chebyshev centers in hyperplanes of $c_0$." Czechoslovak Mathematical Journal 52.4 (2002): 721-729. <http://eudml.org/doc/30738>.
@article{Veselý2002,
abstract = {We give a full characterization of the closed one-codimensional subspaces of $c_0$, in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.},
author = {Veselý, Libor},
journal = {Czechoslovak Mathematical Journal},
keywords = {Chebyshev centers; proximinal hyperplanes; space $c_0$; Chebyshev centers; proximinal hyperplanes; space },
language = {eng},
number = {4},
pages = {721-729},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Chebyshev centers in hyperplanes of $c_0$},
url = {http://eudml.org/doc/30738},
volume = {52},
year = {2002},
}
TY - JOUR
AU - Veselý, Libor
TI - Chebyshev centers in hyperplanes of $c_0$
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 721
EP - 729
AB - We give a full characterization of the closed one-codimensional subspaces of $c_0$, in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.
LA - eng
KW - Chebyshev centers; proximinal hyperplanes; space $c_0$; Chebyshev centers; proximinal hyperplanes; space
UR - http://eudml.org/doc/30738
ER -
References
top- Best simultaneous approximation (Chebyshev centers), Parametric Optimization and Approximation (Oberwolfach 1983), Internat. Ser. Numer. Math. 72, B. Brosowski, F. Deutsch (eds.), Birkhauser-Verlag, Basel, 1985, pp. 19–35. (1985) Zbl0563.41021MR0882194
- 10.1016/0021-9045(84)90011-X, J. Approx. Theory 40 (1984), 364–374. (1984) MR0740649DOI10.1016/0021-9045(84)90011-X
- Existence of Chebyshev centers, best -nets and best compact approximants, Trans. Amer. Math. Soc. 271 (1982), 513–524. (1982) MR0654848
- 10.1007/BF02417105, Ann. Mat. Pura. Appl. 101 (1974), 215–227. (1974) MR0358179DOI10.1007/BF02417105
- The best possible net and the best possible cross section of a set in a normed space, Izv. Akad. Nauk. SSSR 26 (1962), 87–106. (Russian) (1962) Zbl0158.13602MR0136969
- A Course in Optimization and Best Approximation. Lecture Notes in Math. 257, Springer-Verlag, 1972. (1972) MR0420367
- Generalized centers of finite sets in Banach spaces, Acta Math. Univ. Comenian. 66 (1997), 83–115. (1997) MR1474552
- A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers, Arch. Math (to appear). (to appear) MR1967268
- The Chebyshev center in hyperspaces of continuous functions, Funktsional’nyj Analiz, vol. 12, A. V. Štraus (ed.), Ul’janovsk. Gos. Ped. Inst., Ul’janovsk, 1979, pp. 56–68. (Russian) (1979) MR0558342
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