V. Nguyen-Khac, K. Nguyen-Van, “An Infinite-Dimensional Generalization of the Jung theorem”, Mat. Zametki, 2006, Volume 80, Issue 2,Pages <nobr>231

This article is cited in 2 papers

An Infinite-Dimensional Generalization of the Jung theorem

V. Nguyen-Khac^a, K. Nguyen-Van^b

^a Institute of Mathematics, National Centre for Natural Science and Technology
^b Hanoi Pedagogical institute

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.

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

UDC: 514.17

Received: 07.06.2005

DOI: 10.4213/mzm2804