Mathematical Notes

, Volume 80, Issue 1–2, pp 224–232 | Cite as

An infinite-dimensional generalization of the Jung theorem

  • V. Nguen-Khac
  • K. Nguen-Van


A complete characterization of the extremal subsets of Hilbert spaces, which is an infinite-dimensional generalization of the classical Jung theorem, is given. The behavior of the set of points near the Chebyshev sphere of such a subset with respect to the Kuratowski and Hausdorff measures of noncompactness is investigated.

Key words

Jung theorem Jung constant extremal subset of a Hilbert space Chebyshev sphere Kuratowski and Hausdorff noncompactness measures 


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  1. 1.
    W. L. Bynum, “Normal structure coe.cients for Banach spaces,” Pacific J. Math., 86 (1980), 427–436.zbMATHMathSciNetGoogle Scholar
  2. 2.
    A. L. Garkavi, “On Chebyshev centers and convex hulls of set,” Uspekhi Mat. Nauk [Russian Math. Surveys], 19 (1964), no. 6, 139–145.zbMATHMathSciNetGoogle Scholar
  3. 3.
    H. W. E. Jung, “Über die kleinste Kugel, die eine räumliche Figur einschliesst, ” J. Reine Angew. Math., 123 (1901), 241–257.zbMATHGoogle Scholar
  4. 4.
    L. Danzer, B. Grunbaum, and V. Klee, Helly’s Theorem and Its Relatives, Amer. Math. Soc., Providence, R. I., 1963; Russian transl.: Mir, Moscow, 1968.Google Scholar
  5. 5.
    N. A. Routledge, “A result in Hilbert space,” Quart. J. Math., 3 (1952), no. 9, 12–18.zbMATHMathSciNetGoogle Scholar
  6. 6.
    V. I. Berdyshev, “A relationship between the Jackson inequality and a geometric problem,” Mat. Zametki [Math. Notes], 3 (1968), no. 3, 327–338.zbMATHMathSciNetGoogle Scholar
  7. 7.
    J. Daneš, “On the radius of a set in a Hilbert space,” Comment. Math. Univ. Carolin., 25 (1984), no. 2, 355–362.MathSciNetGoogle Scholar
  8. 8.
    N. M. Gulevich, “The radius of a compact set in a Hilbert space,” Zap. Nauchn. Sem. LOMI [J. Soviet Math.], 164 (1988), 157–158.Google Scholar
  9. 9.
    J. R. L. Webb and W. Zhao, “On connections between set and ball measures of non-compactness,” Bull. London Math. Soc., 22 (1990), 471–477.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. Nguen-Khac
    • 1
  • K. Nguen-Van
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Hanoi Pedagogical instituteHanoiVietnam

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