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Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.

Extensions uniformes des formes linéaires positives

Hicham Fakhoury (1973)

Annales de l'institut Fourier

Soit M un sous-espace fermé d’un espace de Banach ordonné V  ; ce travail propose des conditions nécessaires et suffisantes pour qu’il existe a 1 , tel que toute forme linéaire f positive et continue sur M admette une extension linéaire f ˜ positive et continue sur V , vérifiant f ˜ a f . On termine par l’exemple d’un couple ( M , V ) ne possédant pas la propriété précédente bien que toute forme linéaire positive continue sur M se prolonge en une forme linéaire du même type en V .

Extremal solutions of a general marginal problem

Petra Linhartová (1991)

Commentationes Mathematicae Universitatis Carolinae

The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.

Extreme and exposed representing measures of the disk algebra

Alex Heinis, Jan Wiegerinck (2000)

Annales Polonici Mathematici

We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...

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