An analog of the Krein-Mil'man theorem for strongly convex hulls in hilbert space

被引：3

作者：

Balashov, MV ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2002年 / 71卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

Hilbert space; convexity; extreme point; strongly extreme point; R-exposed point; strongly convex hull;

D O I：

10.1023/A:1013970122469

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex R-hull of its R-strong extreme points. R-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex R-hull of a set contains the closure of the convex hull of the set.

引用

页码：34 / 38

页数：5

共 14 条

[1] An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space
M. V. Balashov
[J]. Mathematical Notes, 2002, 71 : 34 - 38
[2] An analog of the Krein-Milman theorem for certain non-compact convex sets
Elliott, George A.
Li, Zhiqiang
Zhao, Xia
[J]. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2021, 15 (03) : 1073 - 1103
[3] A Schur type analysis of the minimal weak unitary Hilbert space dilations of a Krein space bicontraction and the Relaxed Commutant Lifting Theorem in a Krein space setting
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Moran, M. D.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (10) : 2557 - 2586
[4] The separation of convex sets and the Krein–Milman theorem in fuzzy quasi-normed space
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[J]. Computational and Applied Mathematics, 2024, 43
[5] On A Generalized Baillon-Haddad Theorem for Convex Functions on Hilbert Space
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[J]. JOURNAL OF CONVEX ANALYSIS, 2015, 22 (04) : 963 - 967
[6] The separation of convex sets and the Krein-Milman theorem in fuzzy quasi-normed space
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[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (02):
[7] SPECTRAL THEOREM FOR UNBOUNDED STRONGLY CONTINUOUS-GROUPS ON A HILBERT-SPACE
BOYADZHIEV, K
DELAUBENFELS, R
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (01) : 127 - 136
[8] An Analog of the Cameron--Johnson Theorem for Linear ℂ-Analytic Equations in Hilbert Space
D. N. Cheban
[J]. Mathematical Notes, 2000, 68 : 790 - 793
[9] An analog of the Cameron-Johnson theorem for linear C-analytic equations in Hilbert space
Cheban, DN
[J]. MATHEMATICAL NOTES, 2000, 68 (5-6) : 790 - 793
[10] A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space
Bauschke, Heinz H.
Combettes, Patrick L.
Luke, D. Russell
[J]. JOURNAL OF APPROXIMATION THEORY, 2006, 141 (01) : 63 - 69

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