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An extension of the Krein-Milman theorem and applications

University of British Columbia

The Krein-Milman Theorem says that each compact, convex subset of a locally convex space is the closed convex hull of its extreme points. In the case of a separable Banach Space several collections of extreme points are known to be dense in the whole set of extreme points (e.g. the set of exposed points [5; theorem 4]; the set of denting points [8; remarks following definition 44]). Consequently these sets can be used instead of the whole set of extreme points to generate compact convex sets. In this thesis we examine such a dense subset of extreme points in the context of less structured separable locally convex spaces. We also examine some applications of the resulting extended Krein-Milman Theorem.

Text

2010-02-21

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http://hdl.handle.net/2429/20616

Mathematics

University of British Columbia

Graduate