Chebyshev constant for centered sets
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- by Susan L. Friedman PDF
- Proc. Amer. Math. Soc. 50 (1975), 344-350 Request permission
Abstract:
Using $\lambda$th power means in the case $\lambda \geq 1$ it is proven that the Chebyshev constant of any bounded centered set in a metric space is equal to one-half the topological diameter of the set. Thus the Chebyshev constant for any unit ball of a normed linear space is equal to one for the above means.References
- M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), no. 1, 228–249 (German). MR 1544613, DOI 10.1007/BF01504345
- Susan L. Friedman, Chebyshev constant and Chebyshev points, Trans. Amer. Math. Soc. 186 (1973), 129–139 (1974). MR 370365, DOI 10.1090/S0002-9947-1973-0370365-6
- A. L. Garkavi, On the optimal net and best cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87–106 (Russian). MR 0136969
- Einar Hille, Methods in classical and functional analysis, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0463863
- Einar Hille, Topics in classical analysis, Lectures on Modern Mathematics, Vol. III, Wiley, New York, 1965, pp. 1–57. MR 0178099 H. W. E. Jung, Über die kleinste Kugel, die eine raumliche Figur einschliesst, J. für Math. 123 (1901), 241-257. A. N. Kolmogorov and V. M. Tihomirov, $\epsilon$-entropy and $\epsilon$-capacity of sets in function spaces, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 3-86; English transl., Amer. Math. Soc. Transl. (2) 17 (1961), 277-364. MR 22 # 2890; 23 # A2031. G. Pólya and G. Szegö, Über den transfiniten Durchmesser (Kapazitatskonstante) von ebenen und raumlichen Punktmengen, J. Reine Angew. Math. 165 (1931), 4-49.
- A. F. Ruston, A note on the greatest crossnorm, Proc. Amer. Math. Soc. 13 (1962), 828–829. MR 149230, DOI 10.1090/S0002-9939-1962-0149230-3
- Ivan Singer, Best approximation in normed linear spaces by elements of linear subspaces, Die Grundlehren der mathematischen Wissenschaften, Band 171, Publishing House of the Academy of the Socialist Republic of Romania, Bucharest; Springer-Verlag, New York-Berlin, 1970. Translated from the Romanian by Radu Georgescu. MR 0270044
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 344-350
- MSC: Primary 41A45
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370015-6
- MathSciNet review: 0370015