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An infinite-dimensional generalization of the Jung theorem

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Abstract

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.

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Bibliography

  1. W. L. Bynum, “Normal structure coe.cients for Banach spaces,” Pacific J. Math., 86 (1980), 427–436.

    MATH  MathSciNet  Google Scholar 

  2. A. L. Garkavi, “On Chebyshev centers and convex hulls of set,” Uspekhi Mat. Nauk [Russian Math. Surveys], 19 (1964), no. 6, 139–145.

    MATH  MathSciNet  Google Scholar 

  3. H. W. E. Jung, “Über die kleinste Kugel, die eine räumliche Figur einschliesst, ” J. Reine Angew. Math., 123 (1901), 241–257.

    MATH  Google Scholar 

  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. N. A. Routledge, “A result in Hilbert space,” Quart. J. Math., 3 (1952), no. 9, 12–18.

    MATH  MathSciNet  Google Scholar 

  6. V. I. Berdyshev, “A relationship between the Jackson inequality and a geometric problem,” Mat. Zametki [Math. Notes], 3 (1968), no. 3, 327–338.

    MATH  MathSciNet  Google Scholar 

  7. J. Daneš, “On the radius of a set in a Hilbert space,” Comment. Math. Univ. Carolin., 25 (1984), no. 2, 355–362.

    MathSciNet  Google Scholar 

  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. 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.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Hanoi, Vietnam

    V. Nguen-Khac

  2. Hanoi Pedagogical institute, Hanoi, Vietnam

    K. Nguen-Van

Authors
  1. V. Nguen-Khac
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  2. K. Nguen-Van
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Translated from Matematicheskie Zametki, vol. 80, no. 2, 2006, pp. 231–239.

Original Russian Text Copyright © 2006 by V. Nguen-Khac, K. Nguen-Van.

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Nguen-Khac, V., Nguen-Van, K. An infinite-dimensional generalization of the Jung theorem. Math Notes 80, 224–232 (2006). https://doi.org/10.1007/s11006-006-0131-6

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  • DOI: https://doi.org/10.1007/s11006-006-0131-6

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