Encyclopedia

Krein-Milman theorem

Also found in: Wikipedia.

Krein-Milman theorem

[′krīn ′mil·mən ‚thir·əm]
(mathematics)
The theorem that in a locally convex topological vector space, any compact convex set K is identical with the intersection of all convex sets containing the extreme points of K.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in
References in periodicals archive
This result is an extension of the classical Krein-Milman Theorem.
As mentioned in the introduction, several results have been extended to the hyperspace WCC (X): In the next section, we shall further extend the notion of hyperspace and its corresponding topology [T.sub.w] where the underlying space X is a locally convex topological vector space instead of a Banach space and prove an extreme point theorem which is an extension of the classical Krein-Milman Theorem.
AN EXTREME POINT THEOREM ON HYPERSPACE
Given a Banach space E, let [B.sub.E**] denote the unit closed ball of the second dual E**; and let Ext([B.sub.E**]) be the set of all extreme points of [B.sub.E**] (which is of course nonvoid by virtue of the Krein-Milman theorem).
Fixed point properties for semigroups of non-expansive mappings in conjugate Banach spaces
The collection concludes with papers on the theory of complex functions, a proof of the Krein-Milman Theorem, and a review of the influence of Wedderburn on modern algebra.
Exposition by Emil Artin; a selection
By the Hahn-Banach and the Krein-Milman Theorems, E(x) [not equal to] [empty set].
The unicity of best approximation in a space of compact operators
Copyright © 2003-2025 Farlex, Inc Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.