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Non-compact versions of Edwards’ Theorem

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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.

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Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey

    Nihat G. Gogus

  2. Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, NY, 13244, USA

    Tony L. Perkins & Evgeny A. Poletsky

Authors
  1. Nihat G. Gogus
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  2. Tony L. Perkins
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  3. Evgeny A. Poletsky
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Corresponding author

Correspondence to Evgeny A. Poletsky.

Additional 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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Gogus, N.G., Perkins, T.L. & Poletsky, E.A. Non-compact versions of Edwards’ Theorem. Positivity 17, 459–473 (2013). https://doi.org/10.1007/s11117-012-0181-9

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  • DOI: https://doi.org/10.1007/s11117-012-0181-9

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