An infinite-dimensional generalization of the jung theorem

被引：2

作者：

Nguen-Khac, V.

Nguen-Van, K.

机构：

[1] Inst Math, Hanoi 10000, Vietnam

[2] Hanoi Pedagog Inst, Hanoi, Vietnam

来源：

MATHEMATICAL NOTES | 2006年 / 80卷 / 1-2期

关键词：

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

D O I：

10.1007/s11006-006-0131-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：224 / 232

页数：9

共 50 条

[1] An infinite-dimensional generalization of the Jung theorem
V. Nguen-Khac
K. Nguen-Van
[J]. Mathematical Notes, 2006, 80 : 224 - 232
[2] AN INFINITE-DIMENSIONAL SCHOENFLIES THEOREM
SANDERSON, DE
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 148 (01) : 33 - +
[3] INFINITE-DIMENSIONAL ANALOG OF ZIGEL THEOREM
NOVIKOVA, LV
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1982, 16 (02) : 141 - 143
[4] An infinite-dimensional linking theorem and applications
Schechter, M
Zou, WM
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 201 (02) : 324 - 350
[5] An infinite-dimensional LP duality theorem
Clark, SA
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 2003, 28 (02) : 233 - 245
[6] INFINITE-DIMENSIONAL EXTENSION OF A THEOREM OF KOMLOS
BALDER, EJ
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1989, 81 (02) : 185 - 188
[7] An infinite-dimensional generalization of Zenger's lemma
Drnovsek, Roman
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (02) : 1233 - 1238
[8] A GENERALIZATION OF JUNG THEOREM
HENK, M
[J]. GEOMETRIAE DEDICATA, 1992, 42 (02) : 235 - 240
[9] AN EXTENSION OF BURNSIDE THEOREM TO INFINITE-DIMENSIONAL SPACES
LOMONOSOV, V
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1991, 75 (2-3) : 329 - 339
[10] A fixed point theorem for the infinite-dimensional simplex
Rizzolo, Douglas
Su, Francis Edward
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 332 (02) : 1063 - 1070

← 1 2 3 4 5 →