Theorems of Krein Milman type for certain convex sets of functions operators

Robert R. Phelps

Displaying similar documents to “Theorems of Krein Milman type for certain convex sets of functions operators”

On Bárány's theorems of Carathéodory and Helly type

Ehrhard Behrends (2000)

Studia Mathematica

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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...

A hereditary property in locally convex spaces

Manuel Valdivia (1971)

Annales de l'institut Fourier

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If $E$ is an infrabarrelled space, it is proved that any subspace $F$ , of finite codimension, is infrabarrelled.

Positive vector measures with given marginals

Surjit Singh Khurana (2006)

Czechoslovak Mathematical Journal

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Suppose $E$ is an ordered locally convex space, $X_{1}$ and $X_{2}$ Hausdorff completely regular spaces and $Q$ a uniformly bounded, convex and closed subset of $M_{t}^{+} (X_{1} \times X_{2}, E)$ . For $i = 1, 2$ , let $μ_{i} \in M_{t}^{+} (X_{i}, E)$ . Then, under some topological and order conditions on $E$ , necessary and sufficient conditions are established for the existence of an element in $Q$ , having marginals $μ_{1}$ and $μ_{2}$ .

Generalized characterization of the convex envelope of a function

Fethi Kadhi (2002)

RAIRO - Operations Research - Recherche Opérationnelle

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We investigate the minima of functionals of the form $\int_{[a, b]} g (\dot{u} (s)) d s$ where $g$ is strictly convex. The admissible functions $u : [a, b] \to ℝ$ are not necessarily convex and satisfy $u \leq f$ on $[a, b]$ , $u (a) = f (a)$ , $u (b) = f (b)$ , $f$ is a fixed function on $[a, b]$ . We show that the minimum is attained by $\bar{f}$ , the convex envelope of $f$ .

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies $ξ$ on a fixed infinite dimensional vector space $E$ such that $(E, ξ)$ has not the Hahn-Banach extension property but the topological dual ${(E, ξ)}^{'}$ separates points of $E$ from zero is given.