Non-compact versions of Edwards' Theorem

Nihat G. Gogus; Tony L. Perkins; Evgeny A. Poletsky

doi:10.1007/s11117-012-0181-9

Non-compact versions of Edwards' Theorem

Nihat G. Gogus, Tony L. Perkins, Evgeny A. Poletsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards' Theorem.

Original language	English (US)
Pages (from-to)	459-473
Number of pages	15
Journal	Positivity
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s11117-012-0181-9
State	Published - Sep 2013

Keywords

Envelopes
Jensen measures
Representing measures
Superlinear functionals

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

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10.1007/s11117-012-0181-9

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title = "Non-compact versions of Edwards' Theorem",

abstract = "Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards' Theorem.",

keywords = "Envelopes, Jensen measures, Representing measures, Superlinear functionals",

author = "Gogus, {Nihat G.} and Perkins, {Tony L.} and Poletsky, {Evgeny A.}",

note = "Funding Information: N. G. Gogus is supported by the Scientific and Technological Research Council of Turkey related to a Grant project 110T223 and E. A. Poletsky was supported by the NSF Grant DMS-0900877.",

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T1 - Non-compact versions of Edwards' Theorem

AU - Gogus, Nihat G.

AU - Perkins, Tony L.

AU - Poletsky, Evgeny A.

N1 - Funding Information: N. G. Gogus is supported by the Scientific and Technological Research Council of Turkey related to a Grant project 110T223 and E. A. Poletsky was supported by the NSF Grant DMS-0900877.

PY - 2013/9

Y1 - 2013/9

N2 - Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards' Theorem.

AB - Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards' Theorem.

KW - Envelopes

KW - Jensen measures

KW - Representing measures

KW - Superlinear functionals

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U2 - 10.1007/s11117-012-0181-9

DO - 10.1007/s11117-012-0181-9

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AN - SCOPUS:84881547981

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VL - 17

SP - 459

EP - 473

JO - Positivity

JF - Positivity

IS - 3

ER -

Non-compact versions of Edwards' Theorem

Abstract

Keywords

ASJC Scopus subject areas

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