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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2002 Volume 71, Issue 1, Pages 37–42 (Mi mzm326)

This article is cited in 4 papers

An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space

M. V. Balashov

Moscow Institute of Physics and Technology

Abstract: 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.

UDC: 517.977.8

Received: 15.05.2000

DOI: 10.4213/mzm326


 English version:
Mathematical Notes, 2002, 71:1, 34–38

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